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Essays on Market Structure and Technological Innovation

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of

Philosophy in the Graduate School of The Ohio State University

By

Benjamin Christopher Anderson, M.S.

Graduate Program in Agricultural, Environmental and Development Economics

The Ohio State University

2011

Dissertation Committee:

Ian Sheldon, Advisor

Brian Roe

Matthew Lewis

Copyrighted by

Benjamin Christopher Anderson

2011

ii

Abstract

In these essays, I examine the endogenous relationship between market structure

and innovation within industries with product markets characterized by horizontal

and vertical product differentiation and fixed costs which relate R&D investment

and product quality. The theoretical and empirical models build upon Sutton’s

(1991, 1997, 1998, 2007) endogenous fixed cost (EFC) framework. In the first essay,

I develop an EFC model under asymmetric R&D costs that incorporates an

endogenous decision by firms to license or cross-license their technology. In the

second essay, I examine whether a specific industry, agricultural biotechnology, is

characterized by endogenous fixed costs associated with R&D investment.

The theoretical model presents a more general expression of Sutton’s

framework in the sense that Sutton’s results are embedded in the endogenous

licensing model when markets are sufficiently small, when transactions costs

associated with licensing are sufficiently large, or when patent rights are sufficiently

weak. For finitely-sized markets, the presence of multiple research trajectories and

fixed transactions costs associated with licensing raises the lower bound to market

concentration under licensing relative to the bound in which firms invest along a

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single R&D trajectory or in which transactions costs associated with licensing are

negligible. Moreover, I find that the lower bound to R&D intensity is strictly greater

than the lower bound to market concentration under licensing whereas Sutton

(1998) finds equivalent lower bounds. This implies a greater level of R&D intensity

within industries in which licensing is prevalent as innovating firms are able to

recoup more of the sunk costs associated with increased R&D expenditure. Sutton’s

(1998) EFC model predicts that as the size of the market increases, existing firms

escalate the levels of quality they offer rather than permit additional entry of new

firms. This primary result of quality escalation continues to hold when firms are

permitted to license their technology to rivals, but low-cost innovators are able to

increase the number of licenses to high-cost imitators as market size increases.

Prior to estimating the empirical model, I illustrate the theoretical lower

bounds to market concentration implied by an endogenous fixed cost (EFC) model

with vertical and horizontal product differentiation and derive the theoretical lower

bound to R&D concentration from the same model. Using data on field trial

applications of genetically modified (GM) crops, I empirically estimate the lower

bound to R&D concentration in the agricultural biotechnology sector. I identify the

lower bound to concentration using exogenous variation in market size across time,

as adoption rates of GM crops increase, and across agricultural regions.

iv

The results of the empirical estimations imply that the markets for GM corn,

cotton, and soybean seeds are characterized by endogenous fixed costs associated

with R&D investments. For the largest-sized markets in GM corn and cotton seed,

single firm concentration ratios range from approximately .35 to .44 whereas three

firm concentration ratios are approximately .78 to .82. The concentration ratios for

GM soybean seeds are significantly lower relative to corn and cotton, despite greater

levels of product homogeneity in soybeans. Moreover, adjusting for firm

consolidation via mergers and acquisitions does not significantly change the lower

bound estimations for the largest-sized markets in corn or cotton for either one or

three firm concentration, but does increase the predicted lower bound for GM

soybean seed significantly. These results imply that concentration in intellectual

property in soybean varieties is differentially effected by mergers and acquisitions

relative to corn and cotton varieties.

The empirical estimations imply that the agricultural biotechnology sector is

characterized by endogenous fixed costs associated with R&D investments. As firms

are able to increase their market shares by increasing the quality of products

offered, there are incentives for firms to increase their R&D investments prior to

competing in the product market. The lower bound to concentration implies that

even as the acreage of GM crops planted increases, one would not expect a

v

corresponding increase in firm entry. However, the results from the estimations for

GM soybean seeds indicate that concerns for increased concentration of intellectual

property arising from firm mergers and acquisitions may be justified, even though

there is little evidence to support this claim from the corn and cotton seed markets.

Regulators and policymakers will find the results of the theoretical and

empirical models particularly relevant across a variety of industries. The

announcements of license and cross-license agreements between firms within the

same industry are often accompanied by concerns of collusion and anti-competitive

behavior. Moreover, there have been renewed concerns over concentration in

agricultural inputs, and in particular agricultural biotechnology. However, the

theoretical model implies that the ability of firms to license their technology

increases the highest levels of quality offered by providing additional incentives to

R&D for low-cost market leaders. The empirical estimations reveal that the

agricultural biotechnology sector is characterized by endogenous fixed costs thus

implying a greater level of firm concentration than what would be observed in

perfectly competitive or exogenous fixed cost markets.

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Acknowledgments

I would like to thank my committee, Ian Sheldon, Brian Roe, and Matt Lewis, for their

time and advice in helping to guide me through my dissertation at Ohio State. I am

particularly grateful to my advisor Ian for providing me with unconditional support for

the past three years and allowing me to pursue my research interests independently while

continuing to push me to be a better economist. I am also indebted to Brian for his many

insights and terrific comments on my work throughout my time at Ohio State as well as

for his assistance throughout the job market. I am also grateful to the remaining faculty in

the Department of Agricultural, Environmental, and Development Economics at Ohio

State for their advice, guidance, and friendship over the past five years.

There are too many people to whom I am indebted for helping me to become the

academic and person that I am today, but I would be remiss if I did not thank some of

these persons individually. I am grateful to Michael Sinkey for both his friendship and

support over the past few years as well as for the occasional distraction to solve the

problems in the world of sports. I would also like to thank Saif Mehkari for his friendship

and whose advice kept me from putting my interviewers to sleep during my job market

presentations. For putting up with my crazy living habits despite their own objections to

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working at four o’clock in the morning, I want to thank my friends Doug Wrenn and

Peter McGee.

The sacrifices of my family, and especially of my parents, over the past 30 years

have made all of this possible for me. Nothing that I can I write here can express how

lucky and thankful I am to have such understanding and supportive parents. Finally, I am

most grateful to Carolina Castilla for her encouragement, for her refusal to allow me to

take the easy way, and for making me want to become a better economist and person.

Portions of this dissertation were supported by the Agricultural Food

Research Initiative of the National Institute of Food and Agriculture, USDA as part of

Grant #2008-35400-18704. This work has benefitted from feedback from

discussants and participants at various conferences and seminars. All remaining errors

are my own.

viii

Vita

June 28, 1981 ......................................................... Born – Sylvania, Ohio

1999 to 2003 ......................................................... B.S. Business Administration, Ohio

Northern University

2004 to 2006 ......................................................... M.S. Economics, London School of

Economics

2006 to present ................................................... Graduate Associate, Department of

Agricultural, Environmental and

Development Economics, The Ohio State

University

Fields of Study

Major Field: Agricultural, Environmental and Development Economics

ix

Table of Contents

Abstract ....................................................................................................................................... ii

Acknowledgments .................................................................................................................. vi

Vita ............................................................................................................................................. viii

Table of Contents ..................................................................................................................... ix

List of Tables ............................................................................................................................ xii

List of Figures ......................................................................................................................... xiii

CHAPTER 1: Introduction ..................................................................................................... 1

CHAPTER 2: Endogenous Market Structure, Innovation, and Licensing ............ 14

Theoretical Model: Extending Sutton’s Bounds Approach ............................... 15

Basic Framework and Notation ....................................................................................... 15

Licensing in an Endogenous Model of R&D and Market Structure .................... 23

Equilibrium Configurations under Licensing ........................................................ 29

Bounds to Concentration under Licensing ............................................................. 45

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CHAPTER 3: R&D Concentration and Market Structure in Agricultural

Biotechnology .......................................................................................................................... 55

What is Agricultural Biotechnology? ........................................................................ 56

Endogenous Market Structure and Innovation: The “Bounds” Approach ... 60

An Illustrative Model ............................................................................................................ 60

A Lower Bound to R&D Concentration ......................................................................... 75

Empirical Specification ........................................................................................................ 80

Data and Descriptive Statistics ................................................................................... 84

The Market for Agricultural Biotechnology ........................................................... 93

Empirical Results and Discussion ........................................................................... 101

Estimating the Lower Bounds to R&D Concentration ........................................... 101

R&D Concentration in GM Corn Seed........................................................................... 104

R&D Concentration in GM Cotton Seed ....................................................................... 108

R&D Concentration in GM Soybean Seed ................................................................... 111

CHAPTER 4: Conclusions ................................................................................................. 116

References ............................................................................................................................. 121

Appendix A: Chapter 2 Proofs ......................................................................................... 126

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Appendix B: (Sub-)Market Analysis for GM Crops ................................................... 142

Submarket Analysis: State-Level Climate .................................................................. 142

Submarket Analysis: Corn ................................................................................................ 145

Submarket Analysis: Cotton ............................................................................................ 148

Submarket Analysis: Soybean ........................................................................................ 151

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List of Tables

Table 1: Summary of Equilibrium Definitions .......................................................................... 29

Table 2: Firm, Product, and Trajectory Sets .............................................................................. 30

Table 3: Lower Bound Estimation Data Descriptive Statistics .......................................... 90

Table 4: Market Definition Data Descriptions .......................................................................... 92

Table 5: Lower Bound Estimations for GM Corn Seed ........................................................ 107

Table 6: Lower Bound Estimations for GM Cotton Seed .................................................... 110

Table 7: Lower Bound Estimations for GM Soybean Seed ................................................. 114

Table 8: Predicted Lower Bounds for GM Corn, Cotton, and Soybean Seeds ............. 115

xiii

List of Figures

Figure 1: Equilibrium Concentration Levels and Market Size ......................................... 74

Figure 2: Equilibrium R&D Concentration Levels and Market Size ............................... 80

Figure 3: Single-Firm R&D Concentration Ratios and GM Adoption ............................. 89

Figure 4: 2010 Submarket Shares of US Corn Acres Planted .......................................... 96

Figure 5: 2010 Submarket Shares of US Cotton Acres Planted ....................................... 97

Figure 6: 2010 Submarket Shares of US Soybean Acres Planted .................................... 98

Figure 7: Adoption Rates of GM Corn Across Submarkets ........................................... 100

Figure 8: Adoption Rates of GM Cotton Across Submarkets ........................................ 100

Figure 9: Adoption Rates of GM Soybean Across Submarkets ..................................... 101

Figure 10: Corn R&D Concentration and Market Size .................................................. 102

Figure 11: Cotton R&D Concentration and Market Size................................................ 102

Figure 12: Soybean R&D Concentration and Market Size ............................................. 103

Figure 13: Lower Bounds to R&D Concentration in GM Corn Seed............................. 105

Figure 14: Lower Bounds to R&D Concentration in GM Cotton Seed .......................... 109

Figure 15: Lower Bounds to R&D Concentration in GM Soybean Seed ....................... 112

Figure 16: Average Monthly Temperatures Factor Analysis ......................................... 142

Figure 17: Average Monthly Precipitation Factor Analysis (1) ..................................... 143

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Figure 18: Average Monthly Precipitation Factor Analysis (2) ..................................... 143

Figure 19: Average Monthly Drought Likelihood Factor Analysis................................ 144

Figure 20: Corn Seed Market Size Factor Analysis........................................................ 145

Figure 21: Percentage of Planted Corn Acres Treated with Fertilizer ............................ 146

Figure 22: Percentage of Planted Corn Acres Treated with Herbicide ........................... 146

Figure 23: Percentage of Planted Corn Acres Treated with Insecticide ......................... 147

Figure 24: Cotton Seed Market Size Factor Analysis ..................................................... 148

Figure 25: Percentage of Planted Cotton Acres Treated with Fertilizer (1) ................... 149

Figure 26: Percentage of Planted Cotton Acres Treated with Fertilizer (2) ................... 149

Figure 22: Percentage of Planted Cotton Acres Treated with Herbicide ........................ 150

Figure 28: Percentage of Planted Cotton Acres Treated with Insecticide ...................... 150

Figure 29: Soybean Seed Market Size Factor Analysis .................................................. 151

Figure 30: Percentage of Planted Soybean Acres Treated with Fertilizer ...................... 152

Figure 31: Percentage of Planted Soybean Acres Treated with Herbicide ..................... 152

Figure 32: Percentage of Planted Soybean Acres Treated with Insecticide ................... 153

1

CHAPTER 1: Introduction

In 1942, Joseph Schumpeter proposed that more concentrated markets encouraged

additional technological innovation by firms. However, the relationship between

market concentration and R&D intensity, defined respectively as the market share

of the industry-leading firms and the ratio of R&D expenditure to sales, remains an

open research question both theoretically and empirically. The presence of factors

that affect both market structure and the incentives of firms to invest in R&D, such

as differing consumer preferences, horizontal and vertical comparative advantages,

product differentiation, and strategic alliances across firms, confound attempts to

isolate the relationship between of concentration and R&D intensity.

I focus upon understanding the relationship between market concentration

and technological innovation in two ways. First, I incorporate strategic interactions

between firms in the form of technology licensing into a theoretical model in which

market structure, R&D investment, and technology licensing occur endogenously.

Second, I extend the existing literature by examining the theoretical lower bound to

concentration of R&D activity in an endogenous framework and empirically

estimate these lower bounds using data from the agricultural biotechnology market.

2

In the first essay, I develop a theoretical model of endogenous market

structure and fixed (sunk) R&D investment, based on Sutton (1998; 2007), in which

I allow firms to pursue license and cross-license agreements as an alternate form of

market consolidation which is potentially less costly compared to firm integration

via mergers or acquisitions. I argue that a firm’s R&D investment decision is

inseparable from its decision to pursue licensing agreements such that strategic

alliances, market structure, and technological innovation are all determined

endogenously within some equilibrium process. Additionally, by permitting firms to

invest in R&D and license their technology to competitors without restricting the

nature of product market competition, the theoretical model that I develop allows

for a general, yet rich, examination of the relationship between R&D investments

and market structure.

Allowing for licensing, I find that as market size increases, the market share

of the quality leader and industry concentration converge to a lower bound that is

strictly greater than the bound without licensing which is bounded away from the

predictions of perfectly competitive markets. The model also implies that R&D

intensity of market leaders is greater under licensing relative to the case without

licensing as the innovating firms can escalate quality and recoup the additional sunk

R&D costs via licensing to rivals. Taken together, these results imply that analyses of

3

market concentration and innovation should not neglect the importance of strategic

alliances between firms nor should models of licensing and innovation rely solely

upon an exogenously determined market structure.

Anand and Khanna (2000) find that licensing and cross-licensing agreements

are increasingly observed across R&D-intensive industries and constitute between

20-33% of all strategic alliances in R&D-intensive sectors such as: chemicals,

biotechnology, and computers and semiconductors. Consider for instance, the flash

memory industry which is both a heavily concentrated market (with a four firm

concentration ratio upwards of 0.75) and characterized by extensive fixed cost

investments in R&D. Recently, Samsung Electronics, the leader in flash memory

chips, completed patent cross-license agreements with two of its primary

competitors in this industry, Toshiba and SanDisk. As a general model, this analysis

is relevant to any industry characterized by intensive R&D investments,

concentrated market structures, and licensing agreements including the licensing of

genetic traits in agricultural biotechnology between market-leading firms and the

observed patterns of technology licensing between smaller R&D labs and larger

pharmaceutical manufacturers. Generally, the model describes a relationship

between firm concentration, incentives to invest in R&D, and the incentives of firms

4

to pursue license agreements with competitors through an endogenous fixed cost

framework.

This model adds to the literature on market structure and innovation by

allowing for technology licensing, a form of firm consolidation, to be considered

within an endogenous framework. Moreover, I contribute to the literature on

technology licensing by incorporating the decision of firms to both license their

innovations and choose their own level of R&D expenditure into an endogenously-

determined market structure framework. Firms compete vertically in product

quality and horizontally in product attributes, such that the model also provides an

alternate framework that complements the existing literature concerning mixed

models of vertical and horizontal differentiation (Irmen and Thisse, 1998; Ebina and

Shimizu, 2008) and multiproduct competition (Johnson and Myatt, 2006). Moreover,

I contribute to the literature on cross-licensing agreements between competitors by

developing an endogenous model in which cross-licensing arises endogenously from

complementary technologies across firms.

Sutton (1998; 2007) argues that R&D intensity alone is insufficient to

capture all of the relevant aspects of an industry’s technology and that a more

general “bounds” model which permits a range of possible equilibrium

configurations should be considered. However, Sutton’s model does not

5

differentiate between forms of consolidation between firms (i.e. licensing and cross-

licensing agreements, R&D joint ventures, mergers and acquisitions, etc.) within an

industry and the potential impact of these mechanisms upon market structure.

Sutton’s endogenous fixed cost (EFC) model predicts that in certain R&D-intensive

industries, an escalation of fixed (sunk) cost expenditures by existing firms, rather

than entry by new firms, will occur in response to exogenous changes in market size

or available technology. The EFC model thus implies that there exists a lower

“bound” such that as the size of the market increases, market concentration and

R&D intensity do not converge to the levels prescribed by perfect competition. If

firms engage in licensing and cross-licensing agreements, we cannot determine a

priori if market concentration and R&D intensity remain bounded away from, or

converge to, perfectly competitive levels.

I develop a model in which innovating low-cost firms have an incentive to

offer licenses to high-cost rivals in order to deter entry by other low-cost firms

escalating the market-leading level of quality. This is consistent with Gallini (1984)

who finds that incumbent firms have a strategic incentive to license their technology

to potential entrants in order to “share” the market and deter more aggressive entry

via increased R&D expenditures. Moreover, the model is also consistent with

Rockett (1990) who finds that incumbent firms utilize strategic licensing in order to

6

sustain its comparative advantage past the expiration of its patents by facing an

industry comprised of “weak” competitors. Additionally, I draw upon the findings of

Gallini and Winter (1985) that there exist two contrasting effects of licensing: (i)

there is the incentive which successful innovators have to license their technology

out to competitors (originally pointed out by Salant (1984) in the comment on

Gilbert and Newberry’s (1982) preemption model); and (ii) the low-cost firm has an

incentive to offer the high-cost firm a license in order to make additional research

by the high-cost firm unattractive. Specifically, the EFC model under licensing is

largely driven by the second effect which Reinganum (1989) identifies as

“minimizing the erosion of the low-cost firm’s market share while economizing on

development expenditures” (p. 893, 1989).

Within the licensing literature, this analysis is most closely related to that of

Arora and Fosfuri (2003) who develop a model of optimal licensing behavior under

vertically-related markets. Specifically, they examine the role of licensing as a

strategic behavior when multiple holders of a single technology compete not only in

a final-stage product market, but also in a first-stage market for technology. Their

results indicate that lower transactions costs, arising from stronger patent rights,

increase the propensity of firms to license their technology; thereby lowering

overall profits to innovators, reducing the incentives to engage in R&D, and

7

decreasing the rates of innovation compared with what would be observed

otherwise. Moreover, upon allowing for the number of firms to be endogenously

determined, Arora and Fosfuri find that larger fixed costs associated with R&D

reduce both the number of incumbent firms as well as the per-firm number of

licenses. This model relaxes some of the assumptions of Arora and Fosfuri such that:

(i) competitors in the product market engage in their own R&D activities; (ii)

multiple technology trajectories exist within the industry; and (iii) an fully

endogenous model for both market structure as well as the level of R&D investment

is developed.

In the second essay, I empirically estimate the lower bound to R&D

concentration for the agricultural biotechnology sector in order to determine

whether the industry is characterized by endogenous fixed costs and if the observed

pattern of firm consolidation is consistent with an EFC model. Over the past three

decades, the agricultural biotechnology sector has been characterized by rapid

innovation, market consolidation, and a more exhaustive definition of property

rights. Concentration has occurred in both firm and patent ownership with the six-

firm concentration ratios in patents reaching approximately 50% in the U.S. and the

U.K. (Harhoff, Régibeau, and Rockett, 2001) However, increased concentration has

had ambiguous effects on R&D investment as the ratio of R&D expenditure to

8

industry sales (71.4%) remains relatively large (Lavoie, 2004). Using data on field

trial applications for genetically modified (GM) crops, I exploit exogenous variation

in technology and market size across time and submarkets to analyze whether the

agricultural biotechnology is characterized by a lower bound to concentration

consistent with an endogenous fixed cost (EFC) framework.

Prior to estimating the lower bound to R&D concentration for the

agricultural biotechnology industry, I examine an illustrative model of endogenous

fixed costs in an industry characterized by multiple submarkets. I then derive the

theoretical lower bound to R&D concentration under both exogenous and

endogenous fixed costs as implied by Sutton’s (1998) EFC model in order to obtain

the empirical predictions for testing for a lower bound to R&D concentration. Using

cluster analysis, I define regional submarkets for each GM crop type (corn, cotton,

and soybean) based upon observable data on farm characteristics and crop

production practices at the state level.

Ultimately, this leads to a test of the hypothesis that the agricultural

biotechnology sector is characterized by an EFC model through the examination of

data on field trial applications for GM crop release. The Animal and Plant Health

Inspection Service (APHIS) provides data on permit, notification, and petition

applications for the importation, interstate movement, and release of genetically-

9

modified organisms in the US for the years 1985-2010. By classifying the permit

data according to type, I obtain estimates of concentration in intellectual property

within distinct submarkets as a measure of (intermediate) R&D concentration.

Results from the empirical estimations support the hypothesis that the agricultural

biotechnology sector is characterized by endogenous fixed costs to R&D with the

largest effects within the GM corn and cotton seed markets. However, the estimation

results also indicate that within the soybean seed markets, firm merger and

acquisition activity has significantly increased the observed levels of concentration

in intellectual property. These results jointly reveal a difficulty associated with

examinations of the agricultural biotechnology sector; namely, the nature of

technology competition implies a level of concentration is to be expected, but the

level of merger and acquisition activity remains an important determinate into

examinations of concentration in intellectual property.

Rapid technological innovation and observed firm consolidation has led to

several empirical examinations of market structure in the agricultural

biotechnology industry. Fulton and Giannakas (2001) find that the agricultural

biotechnology sector has undergone a restructuring in the form of both horizontal

and vertical integration over the past ten years. The industry attributes consistently

identified by the literature and that factor into the proposed analysis include: (i)

10

endogenous sunk costs in the form of expenditures on R&D that may create

economies of scale and scope within firms1; (ii) seed and agricultural chemical

technologies that potentially act as complements within firms and substitutes across

firms; and (iii) property rights governing plant and seed varieties that have become

more clearly defined since the 1970s. This proposed research extends the stylized

facts for the agricultural biotechnology industry by identifying the relevance of sunk

costs investments in R&D in shaping the observed concentration and distribution of

firms. As Sheldon (2008) identifies, the presence of endogenous sunk costs in R&D

expenditures, high levels of market concentration, and high levels of R&D intensity

in the agricultural biotechnology make this sector a likely candidate to be well-

described by an EFC-type model such as that proposed by Sutton (1998).

In estimating an EFC-type model, this analysis extends the previous work by

considering a more general framework in which concentration and innovation are

jointly determined. Previously, Schimmelpfennig, Pray, and Brennan (2004) tested

Schumpeterian hypotheses regarding the levels of industry concentration and

innovation in biotechnology and found a negative and endogenous relationship

between measures of industry concentration and R&D intensity. Additional stylized

1 In regards to economies of scale and/or economies of scope in agricultural biotechnology, Chen, Naseem, and Pray (2004) find evidence that supports economies of scope as well as internal and external spillover effects in R&D. However, they fail to find any conclusive results concerning economies of scale or correlation between the size of firms and the size of R&D in agricultural biotechnology.

11

examinations of the agricultural biotechnology industry have identified an

endogenous, cyclical relationship between industry concentration and R&D

intensity (Oehmke, Wolf, and Raper, 2005) and categorized the endogenous

relationship between firm innovation strategies, including the role of

complementary intellectual assets, and industry consolidation characteristics

(Kalaitzandonakes and Bjornson, 1997). As a more general model, this analysis

embeds previous results that observe an endogenous relationship between R&D

investments and industry concentration. Moreover, I incorporate exogenous

variations in total market size for each crop type as well as technological

innovations, including the development of second- and third-generation GM crops,

and changes in consumer preferences over the relevant time frame to provide a

richer analysis of industry configurations. Whereas previous examinations have

focused upon identifying the endogenous relationship between R&D intensity and

concentration in agricultural biotechnology, I determine whether (sunk) R&D

investments drive this relationship.

A related vein of research has focused upon the significant levels of merger

and acquisition activity that have historically been observed in the agricultural

biotechnology industry. The explanations behind the high levels of activity have

included the role of patent rights in biotechnology (Marco and Rausser, 2008),

12

complementarities in intellectual property in biotechnology (Graff, Rausser, and

Small, 2003; Goodhue, Rausser, Scotchmer, and Simon, 2002), and strategic

interactions between firms (Johnson and Melkonyan, 2003). This analysis extends

previous examinations into merger and acquisition activity in agricultural

biotechnology in estimating whether this firm consolidation has had a significant

impact upon the observed patterns of R&D concentration while abstaining from

addressing the possible causal mechanisms behind the consolidation activity.

The EFC model employed in this framework has been utilized to empirically

examine a variety of other industries including chemical manufacturing (Marin and

Siotis, 200)), supermarkets (Ellickson, 2007), banking (Dick, 2007), newspapers and

restaurants (Berry and Waldfogel, 2003), and online book retailers (Latcovich and

Smith, 2001). These previous analyses have focused upon examining the

relationship between concentration, captured by the ratio of firm to industry sales,

and investments in either capacity (Marin and Siotis, 2007), product quality

(Ellickson, 2007; Berry and Waldfogel, 2003), or advertising (Latcovich and Smith,

2001). The model of endogenous market structure and R&D investment developed

by Sutton (1998) predicts a lower bound to firm R&D intensity that is theoretically

equivalent to the lower bound to firm concentration under significantly large

markets. To our knowledge, ours is the first examination of a specific industry in the

13

context of firm-level investments in R&D, although the empirical analysis of Marin

and Siotis (2007) of chemical manufacturers does differentiate between product

markets characterized by high and low R&D intensities. Moreover, I contribute to

the industrial organization literature by applying an EFC model to a previously

unexamined industry as well as derive and estimate the lower bound to R&D

concentration under endogenous fixed costs.

In light of the recent Justice Department announcement regarding its

investigations into anticompetitive practices in agriculture2, this analysis is of

interest to both regulators and policymakers concerned with the observed high

levels of concentration in agricultural biotechnology. Specifically, if the agricultural

biotechnology sector is characterized by endogenous fixed costs, the high levels of

concentration, accompanied with high levels of innovative activity, are a natural

outcome of technology competition and are not evidence of collusion among firms.

However, the significant shift in the observed patterns of R&D concentration in

cotton and soybean seed upon accounting for merger and acquisition activity imply

that industry consolidation has increased concentration of intellectual property to

levels greater than what is predicted under endogenous fixed costs alone.

2 Neuman, W. 2010. “Justice Dept. Tells Farmers It Will Press Agricultural Industry on Antitrust.” The New York Times, March 13, pp. 7.

14

CHAPTER 2: Endogenous Market Structure, Innovation, and Licensing

In this chapter, I show that there are incentives for firms with cost advantages to

escalate quality-enhancing investments in R&D and license the increased quality to

high-cost competitors. I derive this result from a theoretical, three-stage model in

which firms first face a market entry choice, and, upon entry, compete first in a

technology market via R&D investment and technology licensing followed by

product market competition given quality choices. The model is fully endogenous in

the sense that market structure, R&D investment, and licensing decisions occur

simultaneously and the model does not rely upon restrictions upon the number of

entrants or the level of R&D investment. Given a set of reasonable assumptions on

the structure of the technology licensing contracts, the model implies that in an

endogenous fixed cost industry, firm concentration will be greater under licensing

relative to the case without licensing and the quality level of the industry-leading

firm will be greater under licensing.

15

Theoretical Model: Extending Sutton’s Bounds Approach

Basic Framework and Notation

Sutton’s (1998; 2007) bounds approach to the analysis of market structure and

innovation considers firm concentration and R&D intensity to be jointly and

endogenously determined in an equilibrium framework. As Van Cayseele (1998)

identifies, the bounds approach incorporates several attractive features to the

analysis of market structure and sunk cost investments; namely it provides

empirically testable hypotheses while permitting a wide class of possible

equilibrium configurations consistent with a diverse contingent of game-theoretic

models. Thus, I adopt the basic endogenous sunk cost framework proposed by

Sutton (1998) as the basis for the theoretical framework incorporating the ability of

firms to license their technology to competitors.

The bounds approach considers firm concentration to be a function of

endogenous sunk costs in R&D investment rather than as being deterministically

driven by exogenous sunk costs. As the level of firm concentration will affect the

incentives to innovate, the endogenous sunk cost framework provides the

16

opportunity for some firms to outspend rivals in R&D and still profitably recover

their sunk cost expenditures. The effectiveness with which firms can successfully

recoup their sunk cost outlays depends upon demand side linkages across products,

the patterns of technology and consumer preferences, and the nature of price

competition. Moreover, the model allows for multiple technology holders to viably

enter into the product market in equilibrium and successfully regain their sunken

investments provided that the market size is sufficiently large.

In building on the framework developed by Sutton (1998), I am interested in

examining an industry characterized by a product market consisting of goods

differentiated both vertically in observable quality and horizontally in observable

attributes. I am thus concerned with some industry consisting of submarkets such

that the quantity of a good in submarket is identified by . In developing an

endogenous fixed cost (EFC) model, Sutton is primarily concerned with the concept

of R&D trajectories and identifying the equilibrium configurations that result from

firms’ R&D activities. He assumes that the industry consists of possible research

trajectories, indexed by , such that each is associated with a distinct submarket.

Thus, each firm invests in one or more research programs, each associated with a

particular trajectory, and achieves a competence (i.e. quality or capability) defined

by an index to be associated with some good .

17

The model developed here diverges from Sutton’s (1998) with respect to the

concepts of product quality and research trajectories primarily in two dimensions:

first, in the definition of quality for some good ; and second, in the relationship

between research trajectories and the associated levels of quality. I consider

multiple attribute products in which the overall quality of some good is

characterized as a function of the technical competencies achieved across all

attributes associated with the good. Specifically, some Firm achieves quality

according to:

where corresponds to the technical competence that Firm achieves along

research trajectory . Therefore, I make the minor distinction between the quality

of a product directly associated with a distinct research trajectory, as is the case in

Sutton’s (1998) model, and the quality of a product as a function of the qualities of

its individual attributes which are directly associated with distinct research

trajectories.3

A firm chooses some value along each trajectory such that

corresponds to inactivity along trajectory and corresponds to a

3 This distinction relates, in part, to the discussion on the possibilities of economies of scope across research trajectories as discussed by Sutton (1998) in Appendix 3.2. Implicit in the model proposed here is the assumption that once firms achieve a level of technical competency along some research trajectory, it can utilize this competency across a broad range of products without incurring additional R&D costs.

18

minimum level of quality required to offer attribute . The quality function is a

mapping for every product such that the shape and characteristics of the

quality function satisfy the following assumptions:

(i) Product quality is concave in individual attributes (i.e.

,

, and

). Thus, firms are limited

in their ability to increase the overall quality level of some

product by escalating the competency they acquire along

a single trajectory;4

(ii) A firm that is inactive along any attribute for some product

achieves a capability equal to the zero (i.e. If

then .). Thus, firms must achieve at least a minimum

level of competency across all trajectories in order to enter

the product market for good ; and

(iii) A capability equal to one, associated with a minimum level

of quality, indicates that a firm has achieved a minimum

level of competency across all trajectories for some

product . (i.e. If then .)

4 In the case in which a product consists of only a single attribute, then the overall level of quality of the product may be increasing at a constant rate. This case is equivalent to the model proposed by Sutton (1998) in which each product is associated with a distinct research trajectory.

19

Thus, there are two possible alternatives with which overall capability achieved by

Firm can be defined: namely, as the -tuple set of qualities that it achieves in each

submarket such that or as the -tuple set of competencies

that it achieves in each trajectory such that . Within the

product market, the primary concern is with the quality levels of the offered

products and the resulting configuration of firms given these qualities. Thus, the

analysis is confined to considering the overall capability that Firm achieves as

being represented by such that corresponds to the case in which

Firm is inactive in every product.

Let be an equilibrium configuration of capabilities that is the outcome of

the R&D process across all firms in an industry. Then is a

vector which consists of the set of capabilities across all active firms . Moreover,

let the industry consist of total firms, with ‘active’ firms in equilibrium, indexed

by such that the costs of R&D investment vary across firms. It is useful to also

specify several other notations regarding capabilities and configurations,

specifically I denote as the set of capabilities of Firm ’s rivals, define

as the maximum level of quality achieved across all firms for

good in some configuration , and define and as the

maximum level of competency achieved within some attribute and across all

20

attributes, respectively. Moreover, let the set of products offered in equilibrium be

, set of products offered by Firm be , the set of products offered by Firm

that contain attribute be , and the total set of attributes possessed by

Firm be .

The profit function and sales revenue for Firm are defined in terms of the

set of firm competencies and the equilibrium configuration . Total profit for

Firm , written in terms of the number of consumers in the market and per

consumer profit , is specified as . Let profit for Firm from a single

product market be specified as . Additionally for some configuration

, I specify the total sales revenue for Firm within a single product market as

, total industry sales summed across all active firms within a single product

market as , and the total industry sales revenue across all

markets, .

Innovation and market structure are endogenous in Sutton’s (1998) bounds

model via the presence of sunk cost investments in technology. Sunk (fixed) costs

are typically industry-specific and can include investments in research laboratories

with a focus upon a specific technology discovery, the adoption of machinery that

offers a cost-reducing process innovation, or marketing, advertising, and branding

campaigns. The model developed here is primarily concerned with R&D

21

investments that lead to products that offer new characteristics and/or improved

quality. Let the sunk (fixed) R&D outlay that achieves technical competency by

Firm along trajectory be expressed as:

I assume that firms incur a minimum setup cost associated with entry in any R&D

trajectory regardless of the level of competency. Moreover, I assume that the fixed

cost schedule is convex (i.e. the elasticity of the fixed cost schedule is greater

than or equal to two) such that the costs of escalating quality increase at least as

rapidly as profits for R&D expenditures above the minimum level; thereby

restricting the ability of firms to infinitely increase the level of product quality they

offer.

I relax the simplifying assumption that firms face symmetric costs (i.e.

) and thus allow for asymmetric costs schedules across firms and

across trajectories, implying that there exist potential costs advantages in R&D. For

simplicity, I assume that along each trajectory there exist two types of firms;

those with a “low” R&D cost parameter within the trajectory and those with a

“high” R&D cost parameter such that

. In equilibrium, there exist

firms with a “low” R&D cost parameter and

firms with a “high” R&D cost

parameter for each trajectory . Additionally, R&D cost parameters across

22

trajectories are assumed to be independent such that the relationship between the

R&D cost parameters of Firms and in trajectory does not correlate with the

relationship between the R&D cost parameters of the firms in trajectory .

The total fixed costs for Firm across all trajectories in which the firm is

active can be expressed as:

Additionally, let the R&D spending by Firm along trajectory , in excess of the

minimum level of investment, be:

such that total R&D spending across all trajectories equals:

where is the total number of trajectories that Firm enters.

Finally, as Sutton (1998) identifies, it is necessary to make additional

assumptions upon the size of the market in order to ensure that the level of sales

sufficient to sustain some minimal configuration such that at least one firm can be

supported in equilibrium. I restrict the domain for the total market size

and assume that the conditions defined by Sutton (1998) in Assumption 3.1 also

hold for our model. Generally, this assumption implies: (i) for every nonempty

23

configuration, industry sales revenue approaches infinity as market size approaches

infinity; and (ii) there is some nonempty configuration that is viable for market sizes

falling within the restricted domain.

Licensing in an Endogenous Model of R&D and Market Structure

In addition to the relaxation of the assumption on symmetric firms and the

(somewhat trivial) clarification regarding the relationship between product quality,

product attributes, and research trajectories, the primary extension of Sutton’s

(1998) model allows firms to acquire attributes either through their own R&D

investments or via the licensing agreements with rivals. Specifically, I permit a

single firm to possess a first-mover advantage in the quality choice decision within

each research trajectory. Thus, the market leader (or “innovator”) decides on the

level of R&D investment that it commits in the given trajectory and whether or not it

will license the technical competency that it attains. All other firms (or “imitators”)

face the decision to enter this research trajectory with their own R&D investment

and incur the associated fixed cost or, if available, to pursue a license agreement to

acquire the level of quality offered by the market leader.

24

For some research trajectory , “imitating” licensee Firm , and “innovating”

licensor Firm , I assume that Firm and Firm can credibly commit to a license

contract that specifies the upfront, lump sum payment, , from Firm to Firm and

the level of competence to be transferred . The assumption of lump sum payments is

consistent with the licensing models developed by Katz and Shapiro (1985) and

Arora and Fosfuri (2003). As Katz and Shapiro (1985) identify, the presence of

information asymmetries over output or imitation of technological innovations

implies that the use of a “fixed-fee” licensing contract is optimal.5 Although the

model is characterized by a lump sum, fixed-fee payment for the license, for

tractability I assume that Firm is able to specify this payment as a proportion of

the sales revenue earned by Firm i along all products which incorporate the licensed

competency along trajectory . The acquisition of a licensed technology is considered

as an alternate to R&D investment while remaining a sunk cost expenditure such

that the payment takes the form:

5 For a counter-argument regarding the feasibility of lump sum payments in licensing contracts, the reader is referred to Gallini and Winter (1985) who assume per unit royalty fees as lump sum payments and two-part tariffs are “institutionally infeasible” (p. 242, 1985). For a more thorough discussion of the pricing of license agreements, please refer to Gallini and Winter (1990).

25

where is the equilibrium configuration of qualities offered under licensing and

is the proportion of sales revenue across all products that

incorporate capability that Firm pays to Firm .

Transactions costs associated with licensing are incorporated into the model

in two ways: first, in the form of a fixed component associated with the formation of

each license agreement; and second, in the imperfect transfer of technical

competencies between firms. I assume that a firm that licenses technology from a

competitor also incurs a fixed transactions cost associated with each license

agreement that is irrecoverable to either contracting firm. This fixed fee can be

thought of as the rents captured by some unrelated, third party intermediary

negotiating the license agreement between the two firms. The fixed transactions

cost and imperfect transfer of technologies introduce inefficiencies into the model

under licensing. However, these inefficiencies are counterbalanced by efficiency

gains as more firms capitalize upon the same R&D expenditures and as high-cost

firms are reduce their inefficient R&D spending such that there is an overall

ambiguous effect.

I account for the variable component of the transactions cost via an imperfect

transfer of technologies between firms. Specifically, some Firm that licenses

competency from Firm is only able to utilize a level of competency equal to

26

, where , without incurring an additional fixed cost of R&D. This

implies that for Firm to achieve the full competency for which it contracted, it must

also incur an additional R&D investment equal to . This imperfect

transfer of technology permits a generalization of the case in which firms incur

additional investments in order to incorporate the licensed competencies into their

own set of offered products.

The total costs associated with Firm licensing competency from Firm

along trajectory , and incurring the additional R&D investment to accommodate

the licensed technology, can thus be expressed as:

In order to examine the feasibility of such license agreements, consider some Firm

that has a high cost to R&D along trajectory such that . Firm faces the

choice between licensing capability from the market leader (and offering a

product with quality ) and producing some capability by investing in its own

R&D (and offering a product with quality ). Given some set of capabilities

across all other trajectories , Firm will (weakly) prefer a license to incurring

the total amount of R&D investment for some quality iff:

27

As firms enter endogenously in equilibrium, the right-hand side of expression

will be zero (i.e. additional firms enter the market until profit net of fixed R&D costs

equals zero). Substituting for and simplifying, I derive an expression for the

proportion of sales revenue accrued to licensor firms which must be satisfied for a

firm with high R&D costs along trajectory to prefer licensing to own R&D. Namely,

For tractability in analysis, consider the special case in which marginal costs of

production are equal to zero such that and let the sales from products

containing attribute equal some proportion of total sales revenue across all

goods. If licensor firms are able to appropriate all excess profits from licensees, the

proportion of sales revenue specified in the licensing agreement can be specified as:

Comparative statics reveal that the proportion of sales revenue that a licensor is

able to capture is decreasing monotonically in the fixed transactions cost parameter

(i.e.

) while it is increasing and concave in the variable

transactions cost parameter (i.e.

and

28

). As , variable transactions costs approach zero

(i.e. more perfect transfer of technology) such that comparative statics on both fixed

and variable transactions costs imply that there is an upper bound on the

proportion of sales revenue that a licensor firm can extract from licensee firms such

that as transactions costs increase.

Moreover, the proportion of revenue that can be appropriated by licensor

firms is also decreasing in the proportion of total licensee sales revenue from

products associated with the licensed competency (i.e.

and

).

This implies that there is a trade-off between “major” innovations in attributes that

can be applied across a broad class of products and the proportion of sales revenue

that can be captured in the licensing of these innovations. This comparative static

result is consistent with the first proposition of Katz and Shapiro (1985) regarding

which innovations will be licensed by firms under a fixed licensing fee and Cournot

competition in the product market. Their first proposition implies that firms will

engage in licensing over minor (or arbitrarily small) innovations, but that major (or

large) innovations will not be licensed. Thus, major innovations which contribute

significantly to total sales revenue will be less likely to be licensed as licensees

would prefer to pursue their own R&D investments in such innovations.

29

Equilibrium Configurations under Licensing

Now I define the conditions that must be satisfied for some configuration to be an

equilibrium without licensing as well as the conditions that must be satisfied for

some configuration to be an equilibrium under licensing. For convenience, Tables

1 and 2 provide a notational summary of equilibrium definitions and firm, product,

and trajectory sets, respectively.

Table 1: Summary of Equilibrium Definitions

Variable Definition

Equilibrium configuration

Equilibrium configurations under licensing

Highest level of quality offered without licensing

Highest competency attained without licensing

Highest level of quality offered under licensing

Highest competency attained under licensing

30

Table 2: Firm, Product, and Trajectory Sets

Variable Definition

Total active firms in equilibrium

Active firms with a low-cost parameter along trajectory

Active firms with a high-cost parameter along trajectory

Products offered by Firm

Products offered by Firm that incorporate attribute

Number of licenses granted for attribute

Set of trajectories in which Firm licenses technology

Set of trajectories in which Firm pursues own R&D

Sutton’s viability condition, or “survivorship principle”, implies that an active Firm

does not earn negative profits net of avoidable fixed costs in equilibrium.

Specifically using the current notation, this condition can be specified as:

Sutton’s (1998) stability condition, or “(no) arbitrage principle”, implies that in

equilibrium, there are no profitable opportunities remaining to permit entry by a

new firm. Specifically, for an entrant firm indexed as Firm , the condition can

be written as:

31

Sutton (1998) provides the proof that any outcome that can be supported as a

(perfect) Nash equilibrium in pure strategies is also an equilibrium configuration

and I forgo any further discussion of the comparability of these results with the

results from purely game theoretic models.

These conditions must also hold for a low-cost Firm producing the highest

level of quality that attains the highest level of competency along some

trajectory . The viability condition implies that this firm earns non-negative profits

such that:

The corresponding stability condition, which precludes a low-cost Firm entering

and escalating quality along trajectory by a factor , is specified as

In order to make these conditions comparable, I assume that firms achieve the same

level of competency along all trajectories . As I allow for asymmetry across

firms in the R&D cost parameter, in equilibrium only firms facing a low-cost R&D

parameter are able to attain the highest levels of competency within any trajectory.

Without the assumption that low-cost firms offer the market-leading levels of

quality in equilibrium, there would exist profitable opportunities for low-cost firms

32

to enter and escalate quality along trajectories in which high-cost firms offered the

highest level of quality.

The assumption of symmetric R&D costs across firms in Sutton (1998)

provides for a tractable examination of market structure and R&D intensity, but is

unable to explain why some industries are characterized by a subset of market

leaders in quality. I relax the assumption of cost symmetry, but restrict the R&D cost

function in two ways. First, if some equilibrium configuration satisfies the stability

condition for all low R&D cost firms, it will also be satisfied for all high R&D cost

firms. Second, a configuration in which a high-cost firm offers the market-leading

quality is not stable to entry (and escalation) by a low-cost firm. One final point of

interest is that the viability and stability conditions allowing for multiple-attribute

products are equivalent to the conditions specified in Sutton (1998) for the subset

of products consisting of a single quality attribute.

There exist stability and viability conditions which must be satisfied for some

configuration to be an equilibrium under licensing.6 For simplicity, I assume that

licensing of competency occurs along trajectory between a firm with a low R&D

cost parameter and firms with high R&D cost parameters. Thus, competitor firms

6 I differentiate these configurations and competencies from those specified by Sutton (1998) as there is no a priori reason to believe that there will be correspondence between the two sets of equilibrium configurations or between the sets of product attributes, although I do anticipate some overlap.

33

are able to cross-license their competencies if there are complementary R&D cost

advantages such that the model predicts increased levels of concentration and

ambiguous effects upon R&D as market-leading, low-cost firms are able to

successfully sustain a “research cartels” across trajectories.

The viability condition for a firm that licenses its technology to rivals can be

expressed as:

Condition implies that every firm that licenses technology in equilibrium

earns non-negative profits. Under licensing, firms may offer similar products which

could lead to an increase in competition, a decrease in consumer prices, and a

potential reduction in per-person consumer profit in the first term of equation

(i.e. “rent dissipation effect”). On the other hand, the final term in equation is

the licensing revenue earned by the innovating firm as summed over all R&D

trajectories and over all firms that license within each trajectory (i.e. “revenue

effect”). The corresponding stability condition for licensor firms is:

The stability condition precludes an additional firm from entering in equilibrium

and recouping the fixed costs associated with entry via licensing its quality to rivals.

34

Similarly, the viability and stability conditions under licensing must hold for

a low-cost licensor Firm that produces the highest level of quality and attains

the highest level of competency along some trajectory . Assuming that the high-

quality firm only licenses the competency that it attains along trajectory and

substituting for the lump-sum licensing payment , the viability condition can

be specified as:

Similarly, the stability condition for licensor firms can be expressed as:

The stability condition under licensing precludes entry by a low-cost

innovating firm that escalates product quality by a factor of and recoups the

additional fixed cost investments via licensing to high-cost rivals. Moreover, I also

specify a stability condition for licensor firms which precludes entry by a low-cost

innovating firm that escalates product quality and chooses not to license to high-

cost rivals. Specifically,

35

Equation implies that, in equilibrium, an innovating firm cannot profitably

enter via quality escalation and not licensing its higher quality when it observes

licensing within the industry. The rent dissipation effect associated with the

licensing of technology or quality to competitors implies that a firm escalating

quality and entering without licensing to competitors earns greater profit relative to

a firm that escalates and enters with licensing. Thus, is necessarily no

greater than such that equation does not cover all potential

profitable opportunities for entry and equation is also necessary.

Let the number of licenses of attribute granted by Firm be equal to

and assume that a potential entrant firm that attempts to escalate quality chooses to

grant the same number of licenses . A firm that licenses technology to competitors

chooses both its level of R&D expenditure and the number of licenses that it offers

and thereby sets the number of rivals that it competes against. By symmetry of

profit functions across firms, I assume that an entrant firm that attempts to establish

a new technology standard along the same trajectory by escalating the capability by

some positive factor will chose the same number of rivals as that chosen by

original firm.

Finally, I make two trivial simplifying assumptions in order to provide

clearer intuition over the viability and stability conditions under licensing. First, I

36

assume that the sales from all of the products that incorporate a licensed attribute

can be expressed as a proportion of total firm sales. Second, I assume zero

marginal costs of production such that firm profit functions and firm sales functions

for some configuration are equivalent. Although zero marginal costs is a

potentially strong assumption, many of the industries with which I am concerned,

including pharmaceuticals, biotechnology, and semiconductors, are characterized by

production processes with negligible or zero marginal costs to production.

Under these two assumptions, the proportion of sales revenue specified by

the lump-sum transfer for the licensing of some attribute with quality to Firm

can be specified as:

Under these additional assumptions, the viability and stability conditions for all

firms that license some attribute with quality can now be characterized as:

37

In order to specify the stability and viability conditions that must be satisfied by

firms that license technology in equilibrium, let the set of trajectories along which

Firm licenses technology be and the set of trajectories along which it invests in

its own R&D be . The licensee viability condition ensures that high-cost firms that

license technology from their low-cost rivals earn profits that cover the fixed R&D

costs along all trajectories in which they do not license technology, the fixed R&D

costs associated with the “catch-up” from the imperfect transfer of technology, the

lump-sum license fee, and the fixed transactions costs associated with licensing.

Thus, for all licensee firms :

Similarly, the stability condition for licensee firms implies that a firm cannot enter

via licensing, invest in its own R&D along the same trajectory, and recoup the costs

associated with licensing and R&D. Namely,

Again, consider the case in which high-cost firms license competency along a

single trajectory , produces quality , and attains the same levels of competency

along every other trajectory . The viability condition can be expressed as:

38

In equilibrium, the stability condition for the licensee must hold such that a firm that

licenses technology from the market leader cannot then escalate the level of quality

provided by escalating its own R&D expenditure. Thus, equilibrium configurations

preclude cases in which licensee firms can acquire technology “cheaply” from rivals

and then pursue their own R&D to escalate the overall level of quality. The explicit

expression of the stability condition in this case is:

I also specify a second stability condition such that a high-cost entrant that licenses

the current maximum quality, escalates this quality through its own R&D, and then

licenses to other high-cost firms is not a feasible equilibrium strategy. Explicitly, this

stability condition can expressed as:

39

Again, under the same assumptions of zero marginal costs and the specification of

sales revenue from associated products as a percentage of total sales revenue, the

viability and stability conditions can be specified as:

For a configuration to be an equilibrium configuration under licensing, the viability

conditions for both licensors and licensees as well as the entire set of

stability conditions must hold. These conditions must hold in

order for there to be an equilibrium without firm entry and exit. If the first (second)

viability condition is violated, then licensing is not profitable or sustainable for the

innovating (imitating) firm. Moreover, if any of the three stability conditions does

not hold, the equilibrium configuration is not stable to entry by a quality-escalating

firm, with or without licensing.

Determining whether the licensor or the licensee conditions will provide the

binding constraint upon the feasible set of equilibrium configurations requires

40

either further restrictions upon the model (i.e. a specific functional form for the

profit function) and/or specific parameter values. However, it is possible to derive a

benchmark in which firms do not license their technology to rivals such that the

relevant viability and stability conditions are and . The feasible set of

equilibrium configurations is defined by the profit function and escalation

parameter such that:

This condition implies that allowing for quality differences in multiple attribute

products decreases the set of feasible equilibrium configurations relative to the case

of single attribute products. Similarly, combining the viability and stability

conditions that must hold for licensor firms yields the expressions:

It is important to note at this time that if ,

then equation describes a more stringent definition of feasible equilibrium

configurations compared to equation . The intuition behind this result is that

in an industry in which firms license in equilibrium under significant rent

41

dissipation effects, it is more profitable for quality-escalating entrants to license

competencies to competitors rather than forgo licensing revenues.

By inspection, the stability condition is a special case of the second

stability condition in which the licensee entrant does not choose to license its

escalated quality. Thus, I derive a similar condition for the feasible set of

equilibrium configurations as determined by the viability and stability

conditions for licensee firms. Namely,

Prior to examining the condition on the feasible set of equilibrium configurations, it

is important to recall that the viability and stability conditions for licensee firms are

defined only over firms with high costs to R&D. For some quality escalation

parameter , the additional fixed cost incurred by firms with high R&D costs is

greater than that incurred by firms with low R&D costs (i.e.

)

since by assumption. The R&D cost asymmetry and fixed transactions costs

with licensing imply that the second term on the right-hand side of equation

42

is greater than the second term on the right-hand side of equations -

and thus a more restrictive set of feasible equilibrium configurations when

transactions costs are large relative to firm profit.

Proposition 1: (Determination of Equilibrium Configurations under Licensing)

Let . If:

and

,

then the set of licensor conditions and bind. If does not hold, but

does, then either the licensor conditions and bind. Otherwise, the

licensee conditions and bind.

Proof of Proposition 1: See Appendix A.

Proposition 1 implies that the relevant licensor stability condition for the binding

set of feasible equilibria will be determined by the rent dissipation effect from

licensing of technology which relates to the competitiveness of the product market.

Rent dissipation from licensing refers to the assumption that the escalating firm’s

43

profit under licensing is no greater than the escalating firm’s profit without

licensing. Thus, the term in the braces on the right-hand side of the first equation is,

by assumption, greater than or equal to 0. As the rent dissipation effect becomes

smaller, the stability condition on a licensing, quality-escalating entrant are more

likely to provide the binding constraint on equilibrium configurations (i.e. if

, then condition characterizes the feasible

equilibrium configurations).

By inspection of Proposition 1, the licensee viability and stability

conditions will define the feasible set of equilibrium configurations

independently of the binding licensor conditions iff:

. Thus, it is possible to interpret when the licensee viability and stability conditions

are likely to provide the binding set of feasible equilibrium strategies. First, for

minor innovations or small escalations of quality (i.e. as from the right-hand

side), the right-hand side of condition on approaches zero such that all fixed-

fee royalty payments offered by licensors will be feasible. As , the

proportion of total sales revenue from products associated with the licensed

attribute becomes small (i.e. ), the viability and stability conditions on

44

licensee firms are less likely to be binding as quality-leading firms would require a

fixed-fee royalty payment that was excessively large.

Thus, attributes that are incorporated into products that contribute to a

small proportion of total licensee sales revenues will be unlikely candidates for

licensing as licensor firms would require high rates of royalty payments. However,

as the proportion of total sales revenue increases, licensor firms require a smaller

proportion of firm profits be appropriated under the licensing agreements. Finally,

as the R&D cost differential between low- and high-cost firms becomes larger,

licensor firms can appropriate a greater proportion of firm sales revenue from the

licensed technology. Thus, as the cost differential between types of firms decreases

such that innovators lose their R&D cost advantage, licensor firms require a smaller

proportion of sales in equilibrium.

Finally, the analysis of the feasible set of equilibrium configurations was

limited to the cases in which licensing occurs. As the configuration of capabilities

with and without licensing, as well as the maximum quality offered, are not

necessarily equivalent, a direct comparison between the feasible set of equilibrium

configurations according to Sutton’s (1998) model under asymmetric costs and

multiple products is uninformative. However, it is important to note that the “No

Licensing” case is implicitly embedded in each of the “Licensing” conditions by

45

either setting the total number of licenses or the fixed-fee royalty payment

equal to zero.

Bounds to Concentration under Licensing

I follow Sutton (1998) in deriving a lower bound theorem under licensing to motive

the analysis of market concentration and the escalation of sunk costs in R&D. The

model without licensing implies a lower bound to market share and R&D/sales ratio

independent of market size. Thus, as market size increases, the market share of the

high quality firm in the endogenous sunk cost industry does not converge to zero,

the result implied by industries characterized by exogenous sunk costs. Thus far, I

have extended Sutton’s (1998) model along three dimensions by incorporating

multiple attribute products, relaxing the assumption on symmetry of R&D costs

across firms, and allowing firms to acquire a product characteristic via licensing

rather than R&D. Given these extensions, I formulate three propositions for the

potential lower bound to concentration as I am unable to distinguish a priori which

of the lower bounds to concentration will be binding.

46

I define the minimum ratio of firm profit to industry sales for every

value of , independently of market size and capability configuration, such that:

Moreover, I also define a corresponding minimum ratio for equilibrium

configurations under licensing for every value of such that:

Thus, for a given configuration under licensing and maximum quality , an

entrant firm chooses to enter with capability along the trajectory which yields

greatest profit . From the definitions of and , this profit is at least

and , respectively, independently from a given configuration

( , ) and market size .

Proposition 2: (Lower Bound under Multiple Attribute Products) Fix any pair

. If is an equilibrium configuration, then the firm that offers the highest

level of quality has market share exceeding exceeding

.


47

Proposition 2 implies that as the market size becomes large, the presence of

multiple attribute products and asymmetric R&D costs alone does not change the

lower bound to the market share of the quality-leading firm relative to that found in

Sutton (1998). For finitely-sized markets however, multiple attributes products

raise the lower bound to concentration such that the share of the market leader is

convergent in market size.

Proposition 3: (Lower Bound under Licensing-1) Fix any pair . If is an

equilibrium configuration under licensing, then the firm that offers the highest level

of quality and licenses its competency to rivals has a share of industry revenue

exceeding

as the size of the market becomes large.


Suppose the proportion of sales revenue that licensor firms can appropriate from

licensee firms is decreasing in technical competency such that a low-cost entrant

that escalates competency along trajectory earns a smaller proportion of

licensee sales revenue. This implies that such that

48

and the lower bound to the market share of the quality-leader is lower under

licensing compared to the case without licensing. Moreover, when is the

relevant stability condition such that Proposition 3 holds, the lower bound to

market share is increasing at a decreasing rate in the number of licenses if

(i.e.

and

). Additional comparative statics on the

proportion of total firm revenue associated with the licensed technology also imply

that the lower bound to market share of the quality leader is increasing at a

decreasing rate in (i.e.

and

).

Proposition 4: (Lower Bound under Licensing-2) Fix any pair . If is an

equilibrium configuration under licensing, then the firm that offers the highest level

of quality and licenses its competency to rivals has a share of industry revenue

exceeding

as the size of the market becomes large.


Unlike the cases in which the licensor stability conditions were the binding

constraints upon equilibrium configurations, the lower bound to market

49

concentration derived from the licensee conditions is not straightforward to

interpret. Specifically under asymmetric R&D costs, the first term in the lower

bound condition in Proposition 4 is strictly less than the first term derived in the

previous propositions as . However, considering the special case in which

the proportion of sales revenue accrued to the licensor is constant (i.e.

), I find that the lower bound under the licensee conditions is greater if

. Comparative statics reveal that this bound is increasing

at a constant rate in the number of licenses (i.e.

) and increasing at an

increasing rate in the proportion of total sales revenue associated with the licensed

technology trajectory (i.e.

and

). Given the lower bound to the share

of industry revenue accrued to the market leader in quality varies if it is derived

from the licensor and licensee stability conditions, I further analyze the potential

embedding of Proposition 3 into Proposition 4 and derive a theorem of non-

convergence under licensing.

50

Theorem 1: (Lower Bound under Licensing) Fix any pair and some

feasible7 royalty payment

. If is an equilibrium

configuration under licensing, then the firm that offers the highest level of quality

and licenses its competency to rivals has a share of industry revenue exceeding:

Corollary to Theorem 1: As , the lower bound to market share converges to

.

All equilibrium configurations with a finitely “small” market size are bounded away

from the convergent threshold by some factor of the fixed transactions costs

associated with licensing and R&D investment along all other trajectories. When

products consist of multiple attributes and there is technology licensing in

equilibrium, the lower bound to market concentration under licensing is greater

7 Here, “feasible” implies that the licensee viability condition is satisfied such that:

.

51

than the lower bound without licensing independently of the size of the market. For

finitely-sized markets, the lower bound is not independent of the size of the market

and strictly greater under positive transactions costs.

Proof of Theorem 1: See Appendix A.

In Theorem 1, I derive the lower bound to concentration under licensing given the

set of propositions over the feasible set of equilibrium configurations and the

respective lower bounds. In the limit as and both approach the lower

bound (i.e.

), then the lower bound under licensing

approaches the lower bound without licensing (if transactions costs are minimal or

market size is large). Additionally, it is interesting to note that lower bound to

market share of the quality leader under licensing embeds the lower bound found

by Sutton (1998) in the case in which the proportion of revenue accrued to the

licensor and the total number of licenses equal zero.

The royalty percentage that a low-cost quality leader can charge to a high-

cost firm for some competency is decreasing at an increasing rate in the number

of licenses granted (i.e.

,

) whereas the lower bound to

concentration is increasing at a constant rate (i.e.

). The first comparative

52

static implies that there is a trade-off in the market share of sales for firms offering

the highest quality with the number of licenses that it grants. The comparative static

on the lower bound to concentration illustrates licensor firms require greater levels

of market concentration in exchange for each additional license.

The lower bound to the ratio of the sales of the high-quality firm to the

industry sales motivates the definition of the escalation parameter alpha. For any

value of , alpha is defined as:

Subsequently, the one-firm sales concentration ratio cannot be less than the

share of industry sales revenue of the high-quality firm. Thus, for any equilibrium

configuration with high quality and competency , is bounded from below by .

In the examination of multiple attribute products without licensing (Proposition 2),

I found a lower bound to concentration that was equivalent to lower bound for

single attribute products under large markets. By fixing the royalty payment and

number of licenses to be zero in Propositions 3 and 4, the lower bound to

concentration without licensing is embedded as a special case of the general model.

However, given that I have determined that the binding conditions on

equilibrium configurations of capabilities under licensing is derived from the

viability and stability conditions of high-cost licensee firms (Theorem 1), I must

53

consider an alternate definition of alpha which incorporates the fixed royalty

payment , the total number of licenses , the proportion of sales of products

associated with the licensed competency , and the level of escalation . For a high-

cost firm, I define the escalation parameter alpha as derived from equation

under sufficiently large market sizes such that:

It is important to note that the definition of is determined by a licensee that

potentially escalates competency (quality) to a level greater than that which has

been licensed. The total number of licenses and the royalty payments are taken as

exogenous to these potential entrants firms. This definition of can be used to

determine a bound to concentration that holds in the limit under no licensing (i.e.

and ) which is equivalent to the condition derived by Sutton

(1998). The lower bound to the R&D/sales ratio for the quality leader for the case in

which the quality leader produces maximum competency along some trajectory

and given some level of competency across all other trajectories can be specified

according to Theorem 2.

54

Theorem 2: (Lower Bound to R&D-Intensity) For any equilibrium configuration

under licensing, the R&D/sales ratio for the low-cost market leader firm, offering

maximum quality by achieving competency

along a single trajectory, is

bounded from below as the size of the market becomes large by:

Proof of Theorem 2: See Appendix A.

Sutton’s (1998) EFC model predicted an identical lower bound to market

concentration and R&D intensity as the size of the market became large. In contrast,

I find that when firms are able to license their technology to competitors, both the

lower bound to market concentration and R&D intensity are greater relative to the

case without licensing, but are no longer identical. Specifically, permitting low-cost

firms to license their technology to high-cost rivals encourages more intensive R&D

as “innovator” firms realize efficiency gains from licensing. Thus, greater market

concentration and more intensive and efficient R&D would have ambiguous effects

upon consumer welfare.

55

CHAPTER 3: R&D Concentration and Market Structure in Agricultural

Biotechnology

In this chapter, I derive and empirically test a lower bound to R&D concentration

upon the theoretical endogenous fixed cost (EFC) model of Sutton (1998). I first

demonstrate the lower bounds to R&D concentration via an illustrative model and

then characterize the empirical predictions from the formal model. I use data on

R&D investments, in the form of field trial applications for genetically modified (GM)

crops, to test for lower bounds to R&D concentration among agricultural

biotechnology firms.

I exploit variation along two dimensions: (i) geographically as adoption rates

for GM crop varieties varies by state and agricultural region; and (ii)

intertemporally as adoption rates for GM crops has been steadily increasing over

time. Moreover, the strengthening of property rights over GM crops over the past 20

years and increased incentives for farmers to plant corn seed, relative to soybean

seed, arising from the subsidies to ethanol production serve as natural experiments

and provide sources of exogenous variation in the market. I estimate the lower

bounds to R&D concentration using a two-step procedure suggested by Smith

56

(1994) in order to test whether the single firm R&D concentration ratios follow an

extreme value distribution.

The econometric results indicate that the markets for corn, cotton, and

soybean seeds are characterized by endogenous fixed costs in R&D with the lower

bound to R&D concentration being greatest for GM corn and cotton seed markets.

Accounting for consolidation of intellectual property via merger and acquisition

activity, the lower bounds to R&D concentration increase significantly for soybean

seed markets. These results imply that the observed concentration in GM seed

varieties can be explained by the nature of technology competition within the

sector, but the patterns of firm consolidation can magnify these results.

What is Agricultural Biotechnology?

Prior to examining market structure and innovation in the agricultural

biotechnology sector, it is important to clearly define what I mean when I use the

term “agricultural biotechnology”. Gaisford, et al. (2001) define biotechnology, in

general terms, as “the use of information on genetically controlled traits, combined

with the technical ability to alter the expression of those traits, to provide enhanced

57

biological organisms, which allow mankind to lessen the constraints imposed by the

natural environment.” For my purposes, I am interested in firms that develop

genetically-modified organisms (GMOs) for commercialization purposes within

agriculture and restrict ourselves primarily to discussion concerning genetically-

modified (GM), or genetically-engineered (GE), crops. Prior to the 1970s, the

development of new plant varieties was largely limited to Mendelian-type genetics

involving selective breeding within crop types and hybridization of characteristics

to produce the desired traits. Generally, it was impossible to observe whether the

crops successfully displayed the selected traits until they had reached maturity

implying a considerable time investment with each successive round of

experimentation. If successful, additional rounds of selective breeding were often

required in order to ensure that the desired characteristics would be stably

expressed in subsequent generations. This process is inherently uncertain as crop

scientists and breeders rely upon “hit-and-miss” experimentation, implying that

achieving the desired outcome might require a not insubstantial amount of time and

resources.

The expansion of cellular and molecular biology throughout the 1960s and

1970s, specifically the transplantation of genes between organisms by Cohen and

Boyer in 1973, increased the ability of crop scientists to identify and isolate desired

58

traits, modify the relevant genes, and to incorporate these traits into new crop

varieties via transplantation with greater precision (Lavoie, 2004). These advances

had two key implications for agricultural seed manufacturers and plant and animal

scientists. First, the ability to identify and isolate the relevant genetic traits greatly

facilitated the transference of desirable characteristics through selective breeding.

Second, the ability to incorporate genetic material from one species into the DNA of

another organism allowed for previously infeasible or inconceivable transfers of

specific traits. Perhaps the most widely known example of this was the

incorporation of a gene from the soil bacterium Bacillus thuringiensis (Bt) that

produces the Bt toxin protein. This toxin is poisonous to a fraction of insects,

including the corn borer, and acts as a “natural” insecticide. When the gene is

incorporated into a plant variety, such as corn, cotton, and now soybeans, the plants

are able to produce their own insecticides, thereby reducing the need for additional

application of chemical insecticides.

GM crops are typically assigned into three broad classifications, termed

“generations”, depending upon the traits that they display and who benefits from

these technological advancements (i.e. farmers, consumers, or other firms). The first

generation consists of crops that display cost- and/or risk-reducing traits that

primarily benefit the farmers, but which also may have important environmental

59

and consumer impacts via decreased application of agricultural chemicals. Specific

examples of first generation crops include herbicide tolerant varieties (i.e. Roundup

Ready® crops), insect resistant varieties (i.e. Bt crops), or crop types that are

particularly tolerant to environmental stresses including drought or flood

(Fernandez-Cornejo and Caswell, 2006). Second generation crops, which are largely

still in development, consist of crops whose final products will deliver some

additional value-added benefits directly to consumers. Products derived from

second generation crops might offer increased nutritional content or other

characteristics that directly benefit the health of end consumers. The third

generation classification captures biotechnology crops developed for

pharmaceuticals, industrial inputs (i.e. specialized oils or fibers), or bio-based fuels.

I focus almost exclusively upon crops within the “first generation” classification as

these constitute the majority of all currently commercialized GM crops. However,

my analysis is applicable to the biotechnology industry in a general sense to the

extent that I identify how the industry has evolved in the past with implications for

how market structure and innovation will evolve as subsequent generations of

biotechnology are introduced.

60

Endogenous Market Structure and Innovation: The “Bounds” Approach

An Illustrative Model

I adapt the theoretical endogenous fixed cost model of market structure and sunk

R&D investments developed by Sutton (1998) and empirically estimate the lower

bounds to R&D concentration in agricultural biotechnology. The empirical

specification that I adopt was developed in Sutton (1991) and has since been

adapted and extended in Giorgetti (2003), Dick (2007), and Ellickson (2007). I

illustrate that the characterization of a market into horizontally differentiated

submarkets does not change the theoretical predictions for the lower bound to

concentration in the largest submarket under endogenous fixed costs. Subsequently,

I derive the theoretical lower bound to R&D concentration for endogenous and

exogenous fixed cost industries and specify the empirically testable hypotheses.

The specification of the empirical model relies upon a set of assumptions

regarding the nature of product differentiation in the agricultural biotechnology

sector. First, I assume that there exist regional variations in the demand for specific

seed traits, such as herbicide tolerance or insecticide resistance, and that these

61

regional variations create geographically distinct submarkets. This assumption

corresponds with the empirical findings of Stiegert, Shi, and Chavas (2011) of spatial

price differentiation in GM corn. Secondly, I assume that farmers value higher

quality products such that a firm competes within each submarket primarily via

vertically differentiating the quality of its seed traits. Thus, I estimate a model of

vertical product differentiation in the agricultural biotechnology sector while

accounting for horizontal differentiation via the definition of geographically distinct

product submarkets.

In order to derive the empirical predictions for the lower bound to R&D

concentration, I adapt the illustrative model developed by Sutton (1991). I assume

that within a regional submarket , there are identical farmers that have a

quality-indexed demand function such that:

where is some “outside” composite good (i.e. fertilizer, machinery, etc.) which is

set as numeraire, is the quantity of the “quality” good (i.e. seeds), is the quality

level associated with good and preferences are captured by the parameter . I

assume a level of quality such that corresponds to a minimum level of

quality in the market and all farmers prefer higher quality for a given set of prices.

The farmer in submarket maximizes across all quality goods such that:

62

where is the total income for the farmer in submarket . Solving reveals that,

independent of equilibrium prices or qualities, the farmer will spend a fraction of

her total income upon the quality good.

I consider a three stage game consisting of: (i) a market entry decision into

some submarket ; (ii) technology market competition in which firms make fixed

R&D investments in product quality; and (iii) product market competition in

quantities. In the second stage, given decisions to enter in the first stage, firms

choose the levels of quality they offer by making deterministic fixed (sunk)

R&D investments within each submarket. In the final stage, firms engage in Cournot

competition over quantities in the product market with the set of product quality

levels taken as given. The farmer thus chooses the good that maximizes the

quality-price ratio such that all firms that have positive sales in equilibrium

have proportionate quality-price ratios (i.e. ).

In order to derive the profit function for firms, consider the case in which all

firms in a submarket are symmetric (i.e. ). It must be the case that the

equilibrium level of prices equals the share of expenditure over total industry

output such that:

63

Now suppose a single firm deviates from the symmetric equilibrium by offering a

quality level such that it faces a price equal to:

It follows that the equilibrium price faced by all other firms can be expressed as:

where is total industry output net the output of the deviating firm and

is the deviating firm output. Assuming that firms face a constant marginal cost

independent of the level of quality offered, the profit functions for the deviating firm

and any non-deviating firm in submarket can thus be expressed, respectively,

as:

and

64

Differentiating and solving for the equilibrium levels of quantity yields the following

expressions for the quantity produced for the deviating firm and non-

deviating firms as a function of quality levels and such that:

and

Substituting the expressions for the equilibrium levels of quantity and

into the expressions for prices and , I derive the equilibrium prices for the

deviating firm and non-deviating firms such that:

and

Thus, the net final-stage profit for the deviating firm in submarket can be

expressed as:

65

This profit function allows for the examination of the case where all firms enter with

symmetric quality (i.e. ) and earn final-stage profits independent of quality

(i.e.

) as well as the case in which firms make fixed (sunk) R&D

investments in quality. Letting the total market size (i.e. ) in submarket

be and summing across all submarkets in which firm is active (i.e ), firm

’s total profit can be expressed as:

Sutton (1998) proposes a specification for product quality given the possibility of

economies of scope across R&D trajectories. If agricultural biotechnology firms

develop seed varieties that share attribute traits in adjoining geographic

submarkets, then such a specification could capture technology spillovers between

submarkets. Therefore, the quality level offered by some firm in submarket can

be expressed as a function of the competencies that the firm achieves along all

research trajectories such that:

66

where is the competency that firm achieves in submarket and is a

measure of economies of scope across competencies.

I assume a R&D cost function that consists of a minimum setup cost

associated with entry in each submarket and a variable component that is

increasing in the level of competency . Thus for a given geographic submarket

(i.e. research trajectory), firm chooses a competency and incurs a sunk R&D

cost equal to:

where is the elasticity of the fixed cost schedule. I assume such that R&D

investment rises with quality at least as fast as profits for a given increase in quality.

I obtain an expression for firm ’s total R&D investment by summing across

geographic submarkets (i.e. research trajectories) such that:

where corresponds to the total number of submarkets that firm enters.

Given the expressions for firm profit and firm R&D costs , the

firm’s payoff function (i.e. the profit function net of fixed R&D investments) for the

second stage quality choice decision can be written as:

67

where firms take the number of entrants in each submarket as given from the

first-stage entry decision.

I assume that each submarket in which firms enter can support at least a

single firm producing minimum quality such that:

Given that the assumption on the size of the market and minimum setup cost for

entry holds, I identify two possible symmetric equilibrium outcomes by solving the

quality choice condition in the second stage. The first case corresponds with a

symmetric equilibrium in which all firms active firms in submarket enter with

minimum quality (i.e. ) and incur only the minimum setup cost such

that:

Condition is equivalent to the case of exogenous fixed costs in which all firms

enter with minimum quality (i.e. ).

68

I define symmetric free entry conditions for each submarket such that

firms enter in the first stage until additional entrants are unable to recoup their

fixed R&D investments in the submarket such that:

I now derive the number of firms that enter in a symmetric equilibrium and

incur only the R&D setup cost by investing in the minimum competency level

( ) in submarket . Therefore, the free entry condition under

exogenous fixed costs by can be expressed as:

Solving condition explicitly for the equilibrium number of firms yields:

which depends upon the market size of submarket (i.e. the number of consumers

, the proportion of income spent on the “quality” good , and the income of

consumers ) and the minimum setup cost .

69

If condition does not hold, then the quality choice condition for a

symmetric equilibrium in which all firms enter with quality greater than the

minimum (i.e. ) can be expressed as:

Condition is the case in which firms make quality-enhancing investments in

R&D such that fixed costs are endogenous. Expressing condition explicitly

yields:

Adding and subtracting

, we can express condition as:

Substituting equation for and adding and subtracting yields:

Letting and

and multiplying both sides by yields:

70

Summing equation across all such that:

Since I am summing across all submarkets in which firm is active, equation

can be simplified such that:

Collecting terms, simplifying, and substituting for yields:

I state the free entry condition, as characterized by equation , when firms

enter symmetrically with competency in submarket explicitly as:

such that summing expression across all submarkets in which some firm is

active (i.e. ) yields:

71

Dividing both sides of the quality choice condition by both sides of the free

entry condition yields an expression for the equilibrium number of firms

across submarkets such that:

Combining terms and rearranging yields:

Suppose the total market size for each submarket are ranked from smallest to

largest such that . Then by summation by parts, equation

can be written as:

Since

is equivalent to total firm profit, dividing equation through by

total profit obtains an expression in terms of the summation of the proportion of

total profit attributed to each submarket such that:

Therefore,

equation can be written as:

72

If fixed costs are exogenous, then the monotonocity of equation implies that

the number of firms that enter in equilibrium in each submarket maintains the same

ordering. Thus, and the second term in equation is non-

negative such that

. On the other hand, Sutton’s EFC model (1991;

1998) implies that the presence of endogenous sunk costs limits the equilibrium

number of firms that can enter even as the market size becomes large. Therefore, for

some critical value of market size , industries switch from being characterized by

exogenous fixed costs to endogenous fixed costs such that .

Provided that the number, and size, of submarkets characterized by endogenous

fixed costs are greater than those characterized by exogenous fixed costs, the

second term in equation is non-positive such that

. Thus, if

the largest submarket is characterized by endogenous (exogenous) fixed costs,

then solving

for

yields the least upper bound (greatest lower

bound) to the number of firms that enter in equilibrium.

The number of firms entering under endogenous fixed costs solves

which can be expressed equivalently as:

73

The roots to the quadratic equation are equal to:

Given the assumption on the cost elasticity parameter , the smaller of the two

roots is always less than one such that the equilibrium number of firms that enter

under endogenous fixed costs equals:

Figure 1 illustrates the lower bound to concentration under exogenous (CEX) and

endogenous (CEN) fixed costs for sets of parameter values . As the R&D cost

parameter increases, the upper limit on the total number of firms that enter in

equilibrium increases such that the lower bound to concentration CEN under

endogenous fixed costs decreases. Moreover, as the minimum setup cost

increases, the total number of firms that enter in equilibrium decreases, hence

shifting the lower bound to concentration CEX under exogenous fixed costs outward.

74

Figure 1: Equilibrium Concentration Levels and Market Size

By equating the equilibrium number of firms from equations and , I

determine the threshold value for the market size whereby a submarket

changes from being characterized by exogenous fixed costs to endogenous fixed

costs. Specifically,

The upshot from this analysis is that for sufficiently sized markets, the ability of

firms to increase quality via fixed (sunk) R&D investments precludes additional

Figure 1: Illustrating equilibrium concentration and market size from the Cobb-Douglas demand example (under symmetric equilibrium and simultaneous entry). The R&D cost parameter β3>β2>β1 illustrates the greater lower bound under lower R&D costs relative to the lower bound under higher R&D costs. The minimum setup cost F3>F2>F1 illustrates the horizontal shift of firm entry associated with greater exogenous sunk costs.

Market Size Γ

Co

nce

ntr

ati

on

CN

CEN(β1)

CEN(β2)

CEN(β3)

CEX(F3)

CEX(F2)

CEX(F1)

1 17

75

entry by new firms such that existing firms capture further expansions of market

size via quality escalation. Thus, even as the size of the market grows large (i.e.

) firm concentration levels remain bounded away from perfectly

competitive levels (i.e. ).

A Lower Bound to R&D Concentration

The illustrative model developed in the previous section relates the number of firms

that enter in equilibrium, hence industry concentration, to total market size and the

endogeneity or exogeneity of sunk R&D expenditures. Sutton (1998) finds that the

lower bound to R&D intensity, measured as the ratio of firm R&D to firm sales, is

equivalent to the lower bound to concentration as markets become large. However,

he does not address the implications of the EFC model upon concentration of R&D

within these industries, which remains as a separate and additional concern in

discussions regarding mergers and acquisitions, as well as patent pools, in

agricultural biotechnology (Moschini, 2010; Dillon and Hubbard, 2010; Moss, 2009).

I draw upon the results of Sutton (1998) in order to determine the empirical

predictions of the EFC model regarding R&D concentration, defined as firm R&D

76

relative to industry R&D. The empirical predictions imply that: (i) the lower bound

to R&D concentration is convergent in market size (i.e. the theoretical lower bound

is not independent of the size of the market as is the case with sales concentration);

and (ii) R&D concentration moves in an opposite direction from firm concentration

with changes in market size such that larger markets are characterized by greater

concentration in R&D.

Drawing upon the non-convergence results (Theorems 3.1-3.5) of Sutton

(1998), the lower bound to the single firm concentration ratio for the quality-

leading firm in submarket can be stated as:

where is some constant for a given set of parameter values and is

independent of the size of the market in endogenous fixed cost industries. The value

of alpha depends upon industry technology, price competition, and consumer

preferences and captures the extent that a firm can escalate quality via R&D

investment and capture greater market share from rivals.

For simplicity of analysis, it will be beneficial to introduce notation for

industry sales revenue and R&D expenditure. Following the notation for the sales

revenue and R&D expenditure for some firm in submarket , I define total

industry sales revenue and R&D expenditure in submarket by summing

77

across all firms such that and . Additionally, I define

the degree of market segmentation (or product heterogeneity) as the

share of industry sales revenue in submarket accounted for by the largest product

category such that:

where corresponds with a submarket in which only a single product is

offered.

Moreover, from Theorem 3.2 implies an equivalent expression for the lower

bound to R&D-intensity for the quality-leading firm such that:

Equation implies that the R&D/sales ratio shares the same lower bound as

the single firm concentration ratio as the size of the market becomes large (i.e.

). Multiplying both sides of equation by yields:

Dividing both sides of equation by total industry sales revenue in submarket

yields:

78

However, free entry in equilibrium implies that total industry sales revenue

equals total industry R&D expenditure such that equation can be written

as:

Defining the ratio of R&D concentration for the quality-leading firm as

,

substituting for condition on the lower bound to the single-firm

concentration ratio, and substituting observable market size for profit yields:

Equation provides the empirically testable hypothesis for endogenous fixed

costs relating the lower bound to concentration in R&D expenditure to market size,

the minimum R&D setup cost, and the level of product heterogeneity. If sunk R&D

costs are endogenous, there would be a nonlinear relationship between the degree

of market segmentation (product homogeneity) and the concentration of R&D

for a given market. Moreover, equation implies a lower bound to the

ratio of R&D concentration that converges to some constant as the size

of the market becomes large. For finitely sized markets though, the lower bound to

R&D concentration is increasing in market size such that R&D expenditures are less

concentrated in smaller sized markets.

79

If the industry is instead characterized by exogenous fixed costs, then the

ratio of R&D concentration in submarket can be expressed as:

For some minimum fixed setup cost , concentration in R&D investments is

decreasing in market size and approaches as market size becomes large and,

contrary to the case of endogenous fixed costs, the R&D concentration under

exogenous fixed costs is greatest in small markets. Figure 2 illustrates the

relationship between R&D concentration and market size for both endogenous and

exogenous fixed cost industries.

Figure 2 compares the lower bounds to R&D concentration for industries

characterized by low and high levels of product heterogeneity for a range of

parameters as market size increases. If an industry is characterized by

homogenous products (i.e. low ), there is no range of such that firms invest more

in R&D in excess of the minimum setup cost associated with entry. However, if an

industry is characterized by differentiated products (i.e. high ) and sufficiently

large , then there is an incentive for firms to escalate R&D investment to increase

product quality such that R&D concentration remains bounded away from zero as

market size increases.

80

Figure 2: Equilibrium R&D Concentration Levels and Market Size

Empirical Specification

Equations and lead directly to the empirically testable hypotheses for

the lower bound to R&D concentration. Specifically, an industry characterized by

endogenous fixed costs in R&D should exhibit a lower bound to R&D concentration

Figure 2: Illustrating equilibrium R&D concentration levels and market size for industries with low (2.a) and high (2.b) levels of product heterogeneity. For homogenous product industries (low h), no value of α would permit endogenous fixed costs such that R&D concentration decreases with market size. For heterogeneous product industries (high h), provided α is sufficiently large, R&D concentration will remain bounded away from zero as market size increases.

Market Size Γ

R&

D C

on

cen

tra

tio

n R

N

R&

D C

on

cen

tra

tio

n R

N

Market Size Γ

(b) High h (a) Low h

17 1 1 17

81

that is non-decreasing in market size whereas R&D concentration in exogenous

fixed cost industries is decreasing in market size. Sutton (1991) derives a formal

test for the estimation of the lower bound to concentration in an industry, based

upon Smith (1985, 1994), in which the concentration ratio is characterized by the

(extreme value) Weibull distribution. As Sutton (1991, 1998) identifies, it is

necessary to transform the R&D concentration ratio such that the predicted

concentration measures will lie between 0 and 1. Specifically, the concentration

measure is transformed according to:8

I follow the functional form suggested by Sutton for the lower bound estimation

such that for some submarket , the concentration ratio is characterized by:

where the residuals between the observed values of R&D concentration and the

lower bound are distributed according the Weibull distribution such that:

8 As the transformed R&D concentration is undefined for values of , I monotonically shift the R&D concentration data by -0.01 prior to the transformation.

82

on the domain . The case of corresponds to the two parameter Weibull

distribution such that nonzero values of the shift parameter represent horizontal

shifts of the distribution. The shape parameter corresponds to the degree of

clustering of observations along the lower bound where as the scale parameter

captures the dispersion of the distribution.

To test for a lower bound to R&D concentration, it is equivalent to test

whether the residuals fit a two or three parameter Weibull distribution, that is to

test whether . However, as Smith (1985) identifies, fitting equation

directly via maximum likelihood estimation is problematic for shape parameter

values .9 Smith (1985, 1994) provides a two-step procedure for fitting the

lower bound that is feasible over the entire range of shape parameter values.

Following the methodology of Giorgetti (2003), I first solve a linear

programming problem using the simplex algorithm to obtain consistent estimators

of in which the fitted residuals are non-negative. Therefore, solves:

9 Specifically, for , the maximum for the likelihood function exists, but it does not have the same asymptotic properties and may not be unique. Moreover, for , no local maximum of the likelihood function exists.

83

From the first step, I obtain parameter estimates for fitted residual values

which can be used to estimate the parameters of the Weibull distribution via

maximum likelihood. Specifically, as there are parameters to be estimated in the

first stage, there will be fitted residuals with positive values. By keeping only

the fitted residuals with strictly greater than zero values, I maximize the log pseudo-

likelihood function:

with respect to in order to test whether , which is equivalent to testing

the two parameter versus three parameter Weibull distribution via a likelihood

ratio test. If the three parameter Weibull cannot be rejected, then this implies the

presence of a horizontal shift in the distribution corresponding to an industry in

which R&D is an exogenously determined sunk cost. In all cases, the likelihood ratio

test fails to reject that the data fits the restricted, two parameter model such that

. For each estimation, I report the likelihood ratio statistic which is distributed

with a chi-squared distribution with one degree of freedom. Finally, I compute

standard errors for the first-stage estimations via bootstrapping and standard

errors for the second-stage estimations according to the asymptotic distributions

defined in Smith (1994).

84

Data and Descriptive Statistics

In order to estimate an endogenous fixed cost model a la Sutton (1991, 1998), it is

necessary to have both firm-level sales data and total market size for each market

that is representative of the entirety of the industry. Although such data are of

limited availability for the agricultural biotechnology sector, estimation of the

endogenous lower bound to R&D concentration in agricultural biotechnology

according to the proposed model is feasible using publicly available data. The model

specifically requires four types of data for each crop type: (i) firm-level data on R&D

investment, (ii) industry-level data on (sub-) market size, (iii) industry-level data on

product heterogeneity, and (iv) industry-level data on the minimum setup costs for

each (sub-) market. Moreover, additional data on agricultural characteristics at the

state level are required in order to separate the agricultural biotechnology sector

into distinct (sub-) markets for each crop type.

Sutton (1998) identifies the potential use of “natural experiments” in order

to empirically identify the lower bound to concentration within a single industry.

The natural experiments that allow for such an analysis occur when there is an

exogenous shift in consumer preferences or an exogenous change in technology,

85

although exogenous changes in market size also prove useful for analysis. For the

empirical analysis of the agricultural biotechnology sector, I utilize two dimensions

of variation in R&D investment and market size by estimating the lower bound

across geographic submarkets as well as over time. In doing so, I am able to

capitalize upon changes in consumer attitudes towards GM crops over time as well

as advances in technology and/or regulation which decrease the fixed costs

associated with R&D. Moreover, geographic and intertemporal variation in market

size permits the theory to be tested across a variety of market sizes. Finally, I am

able to utilize a “natural experiment”, in the form of differential changes in demand

for corn (positive) and soybean (negative) seed in response to an exogenous

increase in the incentives for farmers to grow corn crops for use in ethanol.

The ideal data for the analysis of an endogenous lower bound to R&D

concentration would be R&D expenditures for each product line for every firm in an

industry. Although data at this level of detail is unavailable for the agricultural

biotechnology sector, there is publicly available data that captures proxies for R&D

investment at the firm and product level in the form of patent and/or field trial

applications for GM crops. However, data on crop patent applications is not

available for the years after 2000 and therefore is less useful for an estimation of

lower bounds to concentration for an industry in which there has been considerable

86

consolidation post-2000. Field trial application data are appropriate for the analysis

as it captures an intermediate R&D process which is mandatory for firms that desire

to bring a novel GM crop to market.

In accordance with the Federal Coordinated Framework for the Regulation of

Biotechnology, the Animal and Plant Health Inspection Services (APHIS) regulates

the release of any genetically engineered (GE) organism that potentially threatens

the health of plant life. Specifically, prior to the release of any GE organism, the

releasing agency, either firm or non-profit institution, must submit a permit

application to the Biotechnology Regulatory Services (BRS). These Field Trial

Applications are made publicly available by the BRS in a database that includes

information on all permits, notification, and petition applications for the

importation, interstate movement, and release of GE organisms in the US for the

years 1985-2010. The database includes the institution applying for the permit, the

status of the application, the plant (or “article”) type, the dates in which the

application was received, granted, and applicable, the states in which the crops will

be released, transferred to or originated from, and the crop phenotypes and

genotypes. As of October 2010, there are 33,440 permits or notifications of release

included in the database for all types of crops. After restricting the sample to firms,

87

by eliminating non-profit institutions, and permits or notification involving the

release of GE crops, there are 9936 remaining observations in the database.

The National Agricultural Statistics Service (NASS), a division of the United

States Department of Agriculture (USDA), conducts the annual June Agriculture

Survey in order to obtain estimates of farm acreage for a variety of crops, including

corn, cotton, and soybeans. The NASS reports data on total amount of acreage, both

planted and harvested, in an annual Acreage report that is made publicly available.

Moreover, the Economic Research Service (ERS) also computes yearly seed costs in

dollars per acre based upon survey data collected by the USDA in the crop-specific

Agricultural Resource Management Surveys (ARMS). After adjusting for inflation,

these seed costs are multiplied by the total acres planted for each crop type to arrive

at total market size.

Since 2000, the June Agricultural Survey has also sampled farmers regarding

the adoption of GM seed varieties for corn, cotton, and soybeans across a subsample

of states.10 Using this survey data, ERS computes and reports estimates for the

extent of GM adoption. GM adoption rates are used to obtain total GM acreage

planted, as well as total market size after multiplying by the inflation adjusted dollar

10 NASS estimates that the states reported in the GM adoption tables account for 81-86% of all corn acres planted, 87-90% of all soybean acres planted, and 81-93% of all upland cotton acres planted. For states without an adoption estimate, overall US adoption estimates are used to compute the size of the GM market. Provided rates of adoption or total planted acreage are not significantly greater among these “marginal” states, this imputation will not bias the estimates.

88

cost of seed, to arrive at a measure of GM market size for the lower bound

estimation. Figure 3 plots three-year average one firm concentration ratios and

adoption rates for GM crops for each crop type from 1996-2010. The graph

illustrates two important trends: (i) increasing rates of adoption of GM seed

varieties across time; and (ii) single firm concentration ratios that initially increased

and have remained consistently high across time.

Additionally, the rates of adoption for 2000-2010, as well as the estimates of

GM adoption for the years 1996-1999 from Fernandez-Cornejo and McBride (2002),

are used to construct product heterogeneity indexes for each crop type that vary

across time. By definition, the product heterogeneity index is meant to capture the

percentage of industry sales of the largest product group. Therefore, I treat seed

varieties as homogenous within product groups, defined as conventional, insect

resistant (IR), herbicide tolerant (HT), and “stacked” varieties consisting of IR and

HT traits, and equate the product heterogeneity index to the percentage of acres

accounted for by the largest group.

89

Figure 3: Single-Firm R&D Concentration Ratios and GM Adoption

The final component required for the estimation of the lower bound to R&D

concentration is the minimum setup cost associated with entry into the product

market. I use data reported in the “National Plant Breeding Study” for 1994 and

2001 in order to obtain a proxy for the R&D setup cost for each crop type. The

minimum setup cost is obtained by first summing the total number of public

“scientist years” (SY), those reported by the State Agricultural Experiment Stations

(SAES) and the Agricultural Research Service (ARS), and divide this sum by the total

number of projects reported for both agencies in order to obtain average SY for a

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1996 1998 2000 2002 2004 2006 2008 2010

C_1 (Corn)

C_1 (Cotton)

C_1 (Soy)

GM (Corn)

GM (Cotton)

GM (Soy)

Year

C1,% GM Acres

Planted

Source: Author’s calculations from APHIS and ERS GM crop adoption data.

90

single crop.11 Minimum setup costs are thus obtained by multiplying average SY by

the private industry cost per SY ($148,000) and adjusting for inflation.12 Table 3

reports summary statistics for field trial applications, crop acreage planted, seed

costs, product heterogeneity, and minimum setup costs.

Table 3: Lower Bound Estimation Data Descriptive Statistics

11 A “scientist year” is defined as “work done by a person who has responsibility for designing, planning, administering (managing), and conducting (a) plant breeding research, (b) germplasm enhancement, and (c) cultivar development in one year (i.e. 2080 hours).” 12 Results of the lower bound estimations are robust to an alternate definition based upon public sector cost per SY ($296,750).

Mean Std. Dev. Min. Max.

Field Trial Applications

Corn 318.86 166.46 3.00 606.00 6696.00

Cotton 41.13 23.63 1.00 91.00 946.00

Soybeans 78.32 55.94 4.00 194.00 1723.00

Total Acres Planted (000 acre)

Corn 79945.43 5176.88 71245.00 93600.00 1678854.00

Cotton 13434.61 1994.88 9149.50 16931.40 282126.90

Soybeans 69462.76 7287.88 57795.00 82018.00 1458718.00

Seed Costs ($/acre)

Corn 25.13 7.10 15.65 49.15 -

Cotton 25.46 15.63 7.24 79.55 -

Soybeans 18.34 6.99 7.79 37.28 -

Product Heterogeneity

Corn 0.69 0.24 0.35 1.00 -

Cotton 0.59 0.26 0.31 1.00 -

Soybeans 0.84 0.14 0.64 1.00 -

Minimum Setup Costs ($1000)

Corn 182536.55 27275.81 147843.26 220132.27 -

Cotton 182019.44 27434.03 147424.44 219508.67 -

Soybeans 282336.98 42553.92 228675.42 340487.88 -

Source: Author's estimates

Yearly

TotalVariable

91

The observable data used in the cluster analysis are from the period prior to the

widespread adoption of GM varieties (1990-1995) and covers agricultural

production in all lower, contiguous 48 states (except Nevada), although the extent of

coverage varies by crop and state. The cluster analysis uses data (summarized in

Table 4) that can be broadly classified into two types: (i) state level data that are

constant across crops; and (ii) data that vary by state and crop level. The state level

data include location data (longitude and latitude measured at the state’s geometric

center), climate data (mean monthly temperatures, mean monthly rainfall, and

mean Palmer Drought Severity Index measured by the National Oceanic and

Atmospheric Administration (NOAA) from 1971-2000), and public federal funding

of agricultural R&D, including USDA and CSREES (NIFA) grants, reported by the

Current Research Information System (CRIS) for the fiscal years 1990-1995. The

state/crop level data analyzed include farm characteristics for each crop variety (i.e.

acres planted, number of farms, average farm size, number of farms participating in

the retail market, total sales, and average sales per farm) that are reported by the

USDA in the 1987 and 1992 US Census of Agriculture. Additional data on the

application of agricultural chemicals were collected by the USDA, NASS and ERS, and

92

reported in the Agricultural Chemical Usage: Field Crop Summary for the years 1990-

1995.

Table 4: Market Definition Data Descriptions

Data Description Years Source

Latitude State geographic centroid - MaxMind®

Longitude State geographic centroid - MaxMind®

Size Total area (000s acres) -

2000 Census of Population

and Housing

Temperature Monthly averages (°F) 1971-2000 NOAA

Rainfall Monthly averages (inches) 1971-2000 NOAA

Drought Likelihood Monthly averages (PDSI) 1971-2001 NOAA

R&D

Total public funds for agricultural R&D

(1990 $000s)1990-1995 CRIS

Cropland Total cropland area (000s acres) 1987;1992 Census of Agriculture

Data Description Years Source

Acres Planted* Total area planted (000s acres) 1987;1992 Census of Agriculture

Share of Cropland* Percentage of cropland planted (%) 1987;1992 Census of Agriculture

Farms* Total farms (farms) 1987;1992 Census of Agriculture

Average Farm Size* Average farm size (000s acres) 1987;1992 Census of Agriculture

Farms with Sales* Total farms selling (farms) 1987;1992 Census of Agriculture

Sales* Total sales (1990 $000s) 1987;1992 Census of Agriculture

Average Farm Sales* Average farm sales (1990 $000s) 1987;1992 Census of Agriculture

Fertilizer Usage (3 types)** Percentage of planted acres treated (%) 1990-1995 Agricultural Chemical Usage

Herbicide Usage (All types)** Percentage of planted acres treated (%) 1990-1995 Agricultural Chemical Usage

Insecticide Usage (All types)*** Percentage of planted acres treated (%) 1990-1995 Agricultural Chemical Usage

*: Corn - No NV; Cotton - Only AL, AZ, AR, CA, FL, GA, KS, LA, MS, MO, NM, NC, OK, SC, TN, TX, VA;

Soybean - No AZ, CA, CT, ID, ME, MA, MT, NV, NH, NM, NY, OR, RI, UT, WA, WY

**: Corn - No NV; Cotton - Only AZ, AR, CA, LA, MS, TX; Soybean - No AZ, CA, CO, CT, ID, ME, MA, MT, NV, NH, NM, NY, OR, RI, UT, VT, WA, WV, WY

***: Corn - No NV; Cotton - Only AZ, AR, CA, LA, MS, TX; Soybean - Only AR, GA, IL, IN, KY, LA, MS, MO, NE, NC, OH, SD

Observable Market Characteristics

State Level

State and Crop Level

93

The Market for Agricultural Biotechnology

In estimating an EFC-type model for a single industry, an initial crucial step is the

proper identification of the relevant product markets. The EFC model predicts an

escalation of fixed-cost expenditures for existing firms as market size increases

rather than entry by additional competitors. For the case of retail industries, such as

those examined by Ellickson (2007) and Berry and Waldfogel (2003), markets are

clearly delineated spatially. However, the identification of distinct markets in

agricultural biotechnology is potentially more problematic as investments in R&D

may be spread over multiple geographic retail markets. Moreover, as we only have

data on firm concentration available at the state level, the difficulty associated with

defining relevant markets is exacerbated.

In order to overcome issues associated with the correct market

identification, I first assume that R&D expenditures on GM crops released

domestically can only be recouped on sales within the US. Although somewhat

innocuous for the market for corn seed, this assumption may be overly restrictive

for other crop types including soybeans and cotton. However, disparate regulatory

processes across countries, as well as the significant size of the US market, reveals

94

the importance of the domestic market to seed manufacturers. Moreover, recent

surveys of global agricultural biotechnology indicate that many of the varieties of

GM crops adopted outside of the US have also been developed outside of the US.

(ISAAA, 2010)

I consider a characterization of regional submarkets for each crop variety

derived from statistical cluster analysis of observable characteristics of agricultural

production within each state and crop variety. Cluster analysis is a useful tool in

defining regional submarkets as it captures the “natural structure” of the data across

multiple characteristics. I utilize K-means clustering by minimizing the Euclidean

distance of the observable characteristics for each crop variety and arrive at ten

corn clusters, six soybean clusters, and six cotton clusters.

The goal of cluster analysis is such that objects within a cluster (i.e. states

within a regional submarket) are “close” in terms of observable characteristics

while being “far” from objects in other clusters. Thus, the objective is to define

distinct, exclusive submarkets in the agricultural seed sector by clustering states

into non-overlapping partitions. I assume a “prototype-based” framework such that

every state in some submarket is more similar to some prototype state that

characterizes its own submarket relative to the prototype states that characterize

other submarkets. Therefore, I utilize a K-means approach by defining the number

95

of submarket clusters K for each crop type and minimizing the Euclidean distance

between each state and the centroid of the corresponding cluster. For robustness, I

vary the number of clusters K for each crop type and also consider alternate

definitions for the distance function.

Although there is a considerable amount of observable data on market

characteristics, I encounter an issue with the degrees of freedom required for the

cluster analysis when we include all available data. Specifically, the number of

explanatory variables for the cluster analysis is limited to , where is the

number of observations (i.e. states with observable characteristics) and is the

number of clusters (i.e. submarkets). In order to reduce the problem of

dimensionality in the cluster analysis, I use factor analysis, specifically principal-

components factoring, to create indexes of variables that measure similar concepts

(i.e. reduce monthly temperature averages to a single temperature index) and

thereby reduce the number of explanatory variables.

The cluster analysis of the market for corn seed builds upon the spatial price

discrimination analysis of Stiegert, Shi, and Chavas (2011) by separating the major

corn production regions into “core” and “fringe” states and refining the classification

of the other regions to better account for observed differences in the share of corn

acres planted and proportion of acres with herbicide and pesticide applications

96

prior to the introduction of GM crops. The resulting submarkets, summarized in

Figure 3 with the submarket shares of total US production, reveals that corn

production is heavily concentrated in only thirteen states with Illinois and Iowa

alone accounting for approximately 30% of all production.

Figure 4: 2010 Submarket Shares of US Corn Acres Planted

The cluster analysis for cotton and soybean markets is slightly more problematic as

fewer states farm these crops relative to corn. Regardless, the cluster analysis, along

with robustness checks over the total number of clusters, reveals that the cotton and

West 3.4%

Western Fringe 17.6%

Southern Fringe 9.1%

Core 29.5%

Northern Fringe 13.0%

Eastern Fringe 15.2%

Southern Plains/ Delta

4.9%

Southeast 3.0%

Mid-Atlantic

4.2%

Northeast 0.2%

Source: Authors’ calculations from NASS 2010 Acreage Report.

97

soybean markets can be reasonably divided into six submarkets apiece. However,

there are large differences in the relative size of submarkets in cotton and soybean

production as well as the regions in which production of each crop occurs. Texas

accounts for over half of all planted acreage in cotton with the rest of the production

primarily located in the Mississippi delta and southeast regions (Figure 5). Soybean

production, on the other hand, primarily occurs in corn-producing regions with the

significant overlap between the major corn and soybean producers (Figure 6).

Figure 5: 2010 Submarket Shares of US Cotton Acres Planted

Southwest 3.2%

Southern Plains 5.0%

Delta 10.8% Texas

52.4%

Southeast 20.9%

Atlantic 5.9%


98

Figure 6: 2010 Submarket Shares of US Soybean Acres Planted

Examining rates of GM adoption across submarkets (Figures 7-9) reveals distinct

differences across submarkets for GM corn and cotton seeds, but similar adoption

rates for GM soybean. One possible explanation for the observed differences across

crop types might be the relatively limited number of phenotypes of GM soybean

released in this period such that all regions had a similar preference for insect

Northern Plains 22.4%

Western Core

31.5%

Eastern Core

28.9%

Southern Plains/ Delta

9.1%

Southeast 9.4%

Mid-Atlantic 2.7%


99

resistance.13 Although there is only limited number of states with available data on

the percentage of farm acres planted with soybeans and treated with insecticide

from 1990-1995, only two states (Georgia and Louisiana) reported percentage of

acres treated at greater than 10% with the remaining states (Arkansas, Illinois,

Indiana, Kentucky Mississippi, Missouri, Nebraska, North Carolina, Ohio, South

Dakota) reporting rates that were typically less than 5% of acres treated. These

descriptive statistics contrast greatly with those for cotton, which also had a limited

number of phenotypes released in this period. Texas, which had the lowest rates of

adoption of Bt Cotton, an insect resistant variety, also had the lowest rates of

insecticide application from 1990-1995.

13 For additional descriptive analysis of the geographically distinct submarkets, please refer to “Appendix B: (Sub-)Market Analysis for GM Crops”. Specifically, Appendix B contains maps illustrating the geographical differences in climate and market size for each crop type as well as differences in the application of fertilizers, herbicides, and insecticides by crop.

100

Figure 7: Adoption Rates of GM Corn Across Submarkets

Figure 8: Adoption Rates of GM Cotton Across Submarkets

0.0

0.2

0.4

0.6

0.8

1.0

% A

do

pte

d

Year

Core

W. Fringe

E. Fringe

N. Fringe

S. Fringe

Other States

Total US

0.0

0.2

0.4

0.6

0.8

1.0

% A

do

pte

d

Year

Texas

SE

Delta

Atlantic

S. Plains

SW

Total US

Other States

Source: Author’s calculations from ERS GM crop adoption data.


101

Figure 9: Adoption Rates of GM Soybean Across Submarkets

Empirical Results and Discussion

Estimating the Lower Bounds to R&D Concentration

Prior to estimating the lower bounds to R&D concentration, it is useful to illustrate

why one would expect the agricultural biotechnology sector to be characterized by

endogenous lower bounds. Specifically, Figures 7-9 illustrate the one- and three-

0

0.2

0.4

0.6

0.8

1

% A

do

pte

d

Year

W. Corn Belt

E. Corn Belt

N. Plains

S. Plains/Delta

Mid-Atlantic

Other States

Total US


102

firm R&D concentration ratios relative to market size for each crop type with and

without adjustments for merger and acquisition activity.

Figure 10: Corn R&D Concentration and Market Size

Figure 11: Cotton R&D Concentration and Market Size

0

0.2

0.4

0.6

0.8

1

Market Size (ln $)

R&

D C

on

c.

(R

1)

R&D Shares (Largest Firm)

0

0.2

0.4

0.6

0.81

Market Size (ln $)

R&

D C

on

c.

(R

3)

R&D Shares (Largest 3 Firms)

0

0.2

0.4

0.6

0.8

1

Market Size (ln $)

R&

D C

on

c.

(R

1)


0

0.2

0.4

0.6

0.8

1

Market Size (ln $)

R&

D C

on

c.

(R

3)


Source: Authors’ calculations.

Legend

: 1990-1995

: 1996-2000

: 2001-2005

: 2006-2010

: M&A Adjusted

Black : Smallest Markets

Blue : Medium Markets

Red : Largest Markets

Legend

: 1990-1995

: 1996-2000

: 2001-2005

: 2006-2010

: M&A Adjusted

Black : Smallest Markets

Blue : Medium Markets



22 15

22 15

103

Figure 12: Soybean R&D Concentration and Market Size

Figures 10-12 illustrate that R&D concentration ratios are non-decreasing in market

size for each type of crop regardless of the measure of R&D concentration, therefore

implying a lower bound. However, these descriptive illustrations do not account for

differing levels of product heterogeneity across time and therefore it is not possible

to reconcile these illustrations with the lower bound to R&D concentration implied

by the theory. As such, the following analysis considers eight variations for each

crop type by analyzing both the single and three-firm concentration, concentration

adjusted and unadjusted for merger and acquisition of intellectual property, and

both total market size for each crop as well as the market size for genetically

engineered crops (1996-2000, 2001-2005, 2006-2010). The two-stage estimation

results as well as illustrative figures are presented for each crop type.

0

0.2

0.4

0.6

0.8

1

Market Size (ln $)

R&

D C

on

c.

(R

1)


0

0.2

0.4

0.6

0.8

1

Market Size (ln $)

R&

D C

on

c.

(R

3)



Legend

: 1990-1995

: 1996-2000

: 2001-2005

: 2006-2010

: M&A Adjusted

Blue : Smallest Markets


22 15

104

R&D Concentration in GM Corn Seed

The lower bounds to concentration for corn seed are illustrated in Figure 13 and the

estimation results are presented in Table 5. The results indicate a lower bound to

R&D concentration that is increasing in the size of the market, independent of the

definitions of R&D concentration and market size. These results are consistent with

an endogenous lower bound to R&D concentration as illustrated in Figure 2 in

which concentration is very low in small-sized markets and increasing in market

size, which contrasts with the exogenous lower bound to R&D concentration which

is strictly decreasing in market size. Moreover, factoring merger and acquisition

activity into the measurement of R&D concentration does not significantly change

the estimates for the lower bound to concentration in corn seed. These results imply

that increased concentration of intellectual property in corn seed occur not as a

consequence of merger and acquisition activity, but rather are inherent in the

nature of technological competition.

105

Figure 13: Lower Bounds to R&D Concentration in GM Corn Seed

When interpreting the results of the lower bound estimation, it is important to recall

that the R&D concentration data have been adjusted according to equation

and for the level of product heterogeneity. For large markets, the predicted lower

bound converges to whereas for very small markets, the predicted lower bound

converges to some negative number (i.e. ). This result can be explained by what we

observe in Figures 2 and 10. According to the theory, I am attempting to fit a lower

bound to an industry that is characterized by exogenous fixed costs in smaller-sized

markets and endogenous fixed costs in larger-sized markets such that there is a

Total Market Size (ln $)

R&

D C

on

ce

ntr

ati

on

Adjusted R&D Shares (Largest Firm)

GM Market Size (ln $)

R&

D C

on

ce

ntr

ati

on



R&

D C

on

ce

ntr

ati

on

Adjusted R&D Shares (Largest 3 Firms)

GM Market Size (ln $)R

&D

Co

nc

en

tra

tio

n


Legend *: M&A unadjusted : Unadjusted Lower Bound +: M&A adjusted : Adjusted Lower Bound Source: Author’s calculations

4.5 24 24 2.5

2.5 24 24 4.5

106

structural break for some unidentified level of market size. A more accurate

estimation based upon the observed data could fit a non-linear lower bound to the

data to account for this structural break, although it is difficult a priori to reconcile

such an analysis with the theoretical predictions. Moreover, Figure 13, which plots

the adjusted data, does not necessarily indicate that a non-linear lower bound would

provide a better fit.

In order to interpret the coefficient estimates over the range of possible

market sizes, I consider 10% changes in the market size for both the largest and

smallest submarkets and report the predicted lower bound results in Table 8. In the

largest submarket (Iowa and Illinois), the predicted lower bound of the single firm

R&D concentration ratio ranges from .3776 to .3909 and a 10% increase in market

size increases the lower bound in the range of .0035 to .0049. For the smallest

submarket (Northeast states), the range of predicted single firm R&D concentration

ratios range from .1122 to .2178 and a 10% increase in market size increases the

lower bound by a range from about .0044-.0071. The predicted values of the three

firm R&D concentration ratios range from .7887 to .8152 in large markets and .2409

to .5062 for small markets. A 10% increase in market size increases the lower

bound in small markets between .0102-.0226 and increases the lower bound in

large markets between .0044-.0055.

107

Table 5: Lower Bound Estimations for GM Corn Seed

LR

Concentration Market Size M&A θ0 θ1 γ δ (χ2=1)

Unadjusted -1.714 ** 0.240 ** 0.747 ** 1.925 ** 0.161

0.060 0.006 0.080 0.445

Adjusted -1.444 ** 0.228 ** 0.718 ** 1.913 ** 0.117

0.042 0.005 0.079 0.459

Unadjusted -0.443 ** 0.186 ** 0.710 ** 2.126 ** -0.006

0.034 0.004 0.091 0.601

Adjusted -0.069 * 0.168 ** 0.690 ** 2.118 ** 0.034

0.030 0.004 0.090 0.617

Unadjusted -7.804 ** 0.901 ** 1.007 ** 4.975 ** -0.020

0.148 0.011 0.119 0.846

Adjusted -6.244 ** 0.830 ** 0.946 ** 4.403 ** 0.016

0.119 0.010 0.111 0.801

Unadjusted -3.211 ** 0.725 ** 0.770 ** 4.007 ** 0.022

0.083 0.007 0.112 1.038

Adjusted -1.923 ** 0.625 ** 0.813 ** 4.273 ** -0.030

0.139 0.012 0.116 1.026

Source: Author's estimates.

**,*: Significance at the 99% and 95% levels, respectively.

First-Stage Second-Stage

R1

Total

GM

R3

Total

GM

108

R&D Concentration in GM Cotton Seed

As with the market for corn seed, the estimation of a lower bound to R&D

concentration in cotton seed implies an industry characterized by endogenous fixed

costs to R&D. Figure 14 illustrates lower bounds to R&D concentration that are

again increasing in market size in each estimation. The results, reported in Table 6,

imply a significant and increasing lower bound to R&D concentration that is not

independent of the size of the market (i.e. ). However, when merger and

acquisition activity are accounted for in R&D concentration, the predicted lower

bound for the cotton seed market changes significantly in the three-firm

concentration estimations, thus implying some of the observed concentration in

intellectual property in cotton seed has occurred as a result of firm mergers and

acquisitions and cannot necessarily be attributed to the nature of technology

competition.

109

Figure 14: Lower Bounds to R&D Concentration in GM Cotton Seed

The predicted lower bound to single firm R&D concentration for GM cotton seed

range from .3539 to .4302 for the largest sized market (Texas) and from .2388 to

.2662 for the smallest sized market (Southwest states). A 10% increase in market

size increases the lower bound to concentration from between .0045 to .0081

regardless of the size of the market. Furthermore, the predicted lower bound for the

three firm R&D concentration ratios range from .7811 to .8767 in the largest market

with a 10% increase in market size raising the predicted lower bound by .0042-


R&

D C

on

ce

ntr

ati

on Adjusted R&D Shares (Largest Firm)


R&

D C

on

ce

ntr

ati

on Adjusted R&D Shares (Largest Firm)


R&

D C

on

ce

ntr

ati

on


GM Market Size (ln $)R

&D

Co

nc

en

tra

tio

n



21 3 3 21

21 3 3 21

110

.0063. In the smallest-sized market, the predicted lower bound to the three firm

R&D concentration ratio ranges from .5765 to .6917 and a 10% increase in market

size increases the predicted lower bound by .0074 to .0123.

Table 6: Lower Bound Estimations for GM Cotton Seed

LR


Unadjusted -2.203 ** 0.372 ** 1.260 ** 1.579 ** 0.028

0.121 0.010 0.195 0.277

Adjusted -1.822 ** 0.343 ** 1.405 ** 1.947 ** 0.066

0.123 0.010 0.231 0.313

Unadjusted -1.606 ** 0.328 ** 1.492 ** 2.277 ** 0.058

0.287 0.022 0.281 0.391

Adjusted -0.366 0.233 ** 1.474 ** 2.551 ** 0.010

0.335 0.026 0.289 0.442

Unadjusted -5.459 ** 0.986 ** 1.114 ** 5.166 ** -0.008

0.432 0.042 0.188 1.040

Adjusted -7.426 ** 1.347 ** 1.400 ** 5.101 ** 0.008

0.268 0.019 0.234 0.821

Unadjusted -2.715 ** 0.881 ** 1.328 ** 6.181 ** 0.114

0.428 0.040 0.255 1.234

Adjusted 1.037 * 0.803 ** 1.022 ** 4.656 ** -0.018

0.507 0.041 0.203 1.160



R3

Total

GM


R1

Total

GM

111

Comparing the predicted lower bounds of the corn and cotton seed markets, it is

evident that the lower bound to R&D concentration in cotton seed increases

somewhat more rapidly relative to corn seed. This result can be explained in part by

the proliferation of products in the GM corn seed market (29 GM seed varieties)

relative to the number of GM cotton seeds marketed (11 GM seed varieties).

(Howell, et al., 2009) As the -index decreases with the level of product

heterogeneity, the R&D concentration for GM cotton seed is more likely to be

characterized by endogenous fixed costs.

R&D Concentration in GM Soybean Seed

Unlike the estimations for GM corn and GM cotton seed, the lower bound

estimations for R&D concentration in GM soybean seed, reported in Figure 15 and

Table 10, are more ambiguous. Although six of eight lower bound estimations are

indicative of endogenous fixed costs in R&D with R&D concentration increasing with

market size, the estimations for the GM market are relatively flat and it is not

evident that these estimations are significantly different from zero for feasible

market sizes. Moreover, from the estimations for total market size, the results

112

indicate that even though the market appears to be characterized by endogenous

fixed costs, much of the concentration has occurred as a result of merger and

acquisition activity. Despite relatively high levels of product homogeneity (5 GM

soybean varieties) and data points that imply a lower bound to R&D concentration

in Figure 12, the empirical results provide only partial evidence that the market for

GM soybeans is characterized by endogenous fixed costs. (Howell, et al., 2009)

Figure 15: Lower Bounds to R&D Concentration in GM Soybean Seed


R&

D C

on

ce

ntr

ati

on



R&

D C

on

ce

ntr

ati

on



R&

D C

on

ce

ntr

ati

on Adjusted R&D Shares (Largest 3 Firms)


R&

D C

on

ce

ntr

ati

on Adjusted R&D Shares (Largest 3 Firms)


4 3

4 3

12

12

9

9

113

The predicted lower bound to R&D concentration for GM soybean seeds reveals the

increase in R&D concentration resulting from mergers and acquisitions more clearly

than either the estimations for GM corn or GM cotton seed. Whereas the lower

bound to single firm R&D concentration ranges from .2625-.2998 in the unadjusted

estimations for the largest-sized market, after adjusting for merger and acquisition

activity the predicted lower bound increases to .4616-.5264. Moreover, a 10%

increase in market size increases the predicted lower bound twice as rapidly when

consolidation of intellectual property via mergers and acquisitions is considered.

The estimations for the three firm R&D concentration ratios imply predicted lower

bounds that range from .3539 for the smallest-sized market to .9187 for the largest-

sized market. Contrary to the results for the single firm R&D concentration ratio, the

predicted lower bound when considering mergers and acquisitions is lower.

It is also important to address the similarities and differences in the second-

stage estimations for GM corn, cotton, and soybean seeds. Recall that the parameter

corresponds to the shape of the Weibull distribution such that a lower value of

corresponds to a higher degree of clustering around the lower bound. Additionally,

the scale parameter describes the dispersion of the data. Most interesting are the

results on the shape parameter which imply a high degree of clustering on the

lower bound for all crop types, with cotton being characterized by the least

114

clustering and corn the most. Moreover, is less than two in all 24 estimations

implying that the two-step procedure of Smith (1985, 1994) is appropriate. Finally,

the estimations of the scale parameter indicate a wider dispersion of R&D

concentration in the three-firm estimations relative to the one-firm estimations.

Table 7: Lower Bound Estimations for GM Soybean Seed

LR


Unadjusted -0.450 ** 0.100 ** 1.325 ** 1.015 ** 0.006

0.105 0.014 0.217 0.172

Adjusted -1.990 ** 0.321 ** 1.674 ** 1.092 ** -0.035

0.137 0.017 0.272 0.147

Unadjusted 0.302 0.048 1.261 ** 0.963 ** -0.029

0.191 0.027 0.249 0.201

Adjusted -0.197 0.145 ** 1.410 ** 1.067 ** -0.060

0.127 0.017 0.303 0.198

Unadjusted -1.892 ** 0.383 ** 1.317 ** 2.093 ** -0.033

0.188 0.024 0.213 0.357

Adjusted -6.835 ** 1.091 ** 0.913 ** 2.888 ** -0.053

0.332 0.041 0.168 0.699

Unadjusted 0.317 0.232 ** 1.009 ** 1.609 ** -0.057

0.371 0.049 0.205 0.418

Adjusted 1.048 0.117 1.082 ** 3.727 ** -0.029

0.863 0.119 0.221 0.876




R1

Total

GM

R3

Total

GM

115

Table 8: Predicted Lower Bounds for GM Corn, Cotton, and Soybean Seeds

Unadjusted Adjusted Unadjusted Adjusted Unadjusted Adjusted Unadjusted Adjusted

Bound 0.3909 0.3888 0.3807 0.3776 0.8152 0.8125 0.8141 0.7887

10% Change 0.0049 0.0046 0.0039 0.0035 0.0055 0.0051 0.0045 0.0044

Bound 0.1122 0.1264 0.2025 0.2178 0.2409 0.3103 0.5023 0.5062

10% Change 0.0071 0.0066 0.0050 0.0044 0.0226 0.0189 0.0120 0.0102

Bound 0.4302 0.4166 0.3983 0.3539 0.7835 0.8767 0.7811 0.8228

10% Change 0.0063 0.0060 0.0059 0.0045 0.0063 0.0049 0.0057 0.0042

Bound 0.2662 0.2635 0.2419 0.2388 0.5765 0.6917 0.5933 0.6884

10% Change 0.0081 0.0075 0.0074 0.0053 0.0123 0.0122 0.0106 0.0074

Bound 0.2625 0.5264 0.2998 0.4616 0.6631 0.9187 0.7140 0.6323

10% Change 0.0045 0.0092 0.0021 0.0048 0.0078 0.0053 0.0040 0.0026

Bound 0.1251 0.1818 0.2422 0.3162 0.3539 0.4790 0.5808 0.5539

10% Change 0.0128 0.0378 0.0022 0.0060 0.0354 0.0773 0.0059 0.0032

Source: Author's estimates

3 Firm R&D Concentration

Total Market GM Market

Merger & Acquisition Merger & Acquisition

Total Market

Merger & Acquisition Merger & Acquisition

GM Market

1 Firm R&D Concentration

Soybean

Largest

Market

Smallest

Market

Largest

Market

Smallest

Market

Corn

Cotton

Largest

Market

Smallest

Market

116

CHAPTER 4: Conclusions

In these essays, I examine the endogenous relationship between market structure

and innovation within industries with product markets characterized by horizontal

and vertical product differentiation and fixed costs which relate R&D investment

and product quality. The theoretical and empirical models build upon Sutton’s

(1991, 1997, 1998, 2007) endogenous fixed cost (EFC) framework.

In the first essay, I develop an EFC model under asymmetric R&D costs that

incorporates an endogenous decision by firms to license or cross-license their

technology. The model presents a more general expression of Sutton’s framework in

the sense that Sutton’s results are embedded in the endogenous licensing model

when markets are sufficiently small, when transactions costs associated with

licensing are sufficiently large, or when patent rights are sufficiently weak. For

finitely-sized markets, the presence of multiple research trajectories and fixed

transactions costs associated with licensing raises the lower bound to market

concentration under licensing relative to the bound in which firms invest along a

single R&D trajectory or in which transactions costs associated with licensing are

negligible. Moreover, I find that the lower bound to R&D intensity is strictly greater

than the lower bound to market concentration under licensing whereas Sutton

117

(1998) finds equivalent lower bounds. This implies a greater level of R&D intensity

within industries in which licensing is prevalent as innovating firms are able to

recoup more of the sunk costs associated increased R&D expenditure and higher

quality.

The results of the theoretical model are consistent with previous models of

strategic licensing between competitors in which the availability of licensing creates

incentives for firms to choose their competition as well as economize on R&D

expenditures. Namely, I find that given sufficiently strong patent protection, it can

be profitable for low-cost “innovating” firms to increase R&D expenditure and

license the higher level of quality to a fewer number of high-cost “imitating” firms

than would enter endogenously without licensing. Sutton’s (1998) EFC model

predicts that as the size of the market increases, existing firms escalate the levels of

quality they offer rather than permit additional entry of new firms. This primary

result of quality escalation continues to hold when firms are permitted to license

their technology to rivals, but low-cost innovators are able to increase the number

of licenses to high-cost imitators as market size increases.

Regulators and policymakers will find these results particularly relevant as

the announcements of license and cross-license agreements between firms within

the same industry are often accompanied by concerns of collusion and anti-

118

competitive behavior. As I have shown however, the ability of firms to license their

technology increases the highest levels of quality offered by providing additional

incentives to R&D for low-cost market leaders. Without an explicit expression of the

functional form of the utility function, I am unable to determine the welfare effects

of higher market concentration, accompanied by higher levels of R&D investment

and product quality. Thus, the consumer welfare effects of an endogenous market

structure and innovation under asymmetric R&D costs and licensing remains an

open area for future research.

In the second essay, I examine whether a specific industry, agricultural

biotechnology, is characterized by endogenous fixed costs associated with R&D

investment. In a mixed model of vertical and horizontal product differentiation, I

illustrate the theoretical lower bounds to market concentration implied by an

endogenous fixed cost (EFC) model and derive the theoretical lower bound to R&D

concentration from the same model. Using data on field trial applications of

genetically modified (GM) crops, I estimate the lower bound to R&D concentration

in the agricultural biotechnology sector. I identify the lower bound to concentration

using exogenous variation in market size across time, as adoption rates of GM crops

increase, and across agricultural regions.

119

The results of the empirical estimations imply that the markets for GM corn,

cotton, and soybean seeds are characterized by endogenous fixed costs associated

with R&D investments. For the largest-sized markets in GM corn and cotton seed,

single firm concentration ratios range from approximately .35 to .44 whereas three

firm concentration ratios are approximately .78 to .82. The concentration ratios for

GM soybean seeds are significantly lower relative to corn and cotton, despite greater

levels of product homogeneity in soybeans. Moreover, adjusting for firm

consolidation via mergers and acquisitions does not significantly change the lower

bound estimations for the largest-sized markets in corn or cotton for either one or

three firm concentration, but does increase the predicted lower bound for GM

soybean seed significantly. These results imply that concerns of concentration of

intellectual property resulting from mergers and acquisitions in agricultural

biotechnology are more important for some crop types relative to others.

The empirical estimations imply that the agricultural biotechnology sector is

characterized by endogenous fixed costs associated with R&D investments. As firms

are able to increase their market shares by increasing the quality of products

offered, there are incentives for firms to increase their R&D investments prior to

competing in the product market. The lower bound to concentration implies that

even as the acreage of GM crops planted increases, one would not expect a

120

corresponding increase in firm entry. However, the results from the estimations for

GM soybean seeds indicate that concerns for increased concentration of intellectual

property arising from firm mergers and acquisitions may be justified, even though

there is little evidence to support this claim from the corn and cotton seed markets.

Given the increased concerns over concentration in agricultural inputs, and

in particular in agricultural biotechnology, regulators and policymakers alike will

find these results of particular interest. Whereas increased levels of concentration

are often associated with an anticompetitive industry, the presence of endogenous

fixed costs and the nature of technology competition in agricultural biotechnology

imply a certain level of concentration is to be expected. Specifically, R&D activity is

concentrated within three to four firms across corn, cotton, and soybeans and the

ratios of concentration have been changing little over the past 20 years. Moreover,

the empirical model leaves open the possibility that the introduction of second and

third generation GM varieties, the opening of foreign markets to GM crops, future

exogenous shocks to technology, or reductions in regulatory cost could lead to

additional entry, exit, or consolidation in the industry.

121

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126

Appendix A: Chapter 2 Proofs

Proof to Proposition 1: In order to derive the first condition in Proposition 1, I

compare the conditions on the feasible set of equilibrium as characterized by

equations and . As the left-hand side and fixed-cost term on the right-

hand side are equivalent across equations, I focus upon the relationship between

and . The larger of these two terms will

determine which of the stability conditions will be binding upon low-cost firms. As

these relationships hold for all values of the escalation parameter , I can derive

an expression for the proportion of sales revenues accrued to innovating firms in

licensing agreements. Specifically this depends upon:

The expression on the right-hand side of equation is non-negative for any

positive rent dissipation effect. The rent dissipation effect falls directly out of the

profit function such that equation implies the first licensor stability

condition will bind over the second licensor stability condition if the

right-hand side is less than or equal to .

127

Without the assumption of either an explicit functional form on the per-

consumer profit function or the nature of competition in the product market, I

cannot determine if the rent dissipation effect will be large or small. However, if

product market competition is intense such that the rent dissipation effect is large, it

can be inferred that

is likely to be observed as is

bounded between 0 and 1. If the product market competition is not strong such that

rent dissipation is weak, the converse likely holds such that first licensor stability

condition will be binding.

If the second stability condition on licensor firms is to bind, then equation

specifies the feasible set of equilibrium configurations as the first term on the

right-hand side is no less than the first right-hand side term in equation . This

condition will be binding under intense product market competition and large rent

dissipation effects.

The second part of Proposition 1 is derived by comparing condition

and . Assuming that market size and firm profits are sufficiently large relative

to fixed cost expenditures along other trajectories and fixed transactions costs

associated with licensing, comparing the coefficients on the first terms yields the

following relationship:

128

If the left-hand side is greater than or equal to the right-hand side, then the licensor

viability and stability conditions provide a more restrictive set of feasible

equilibrium configurations independently of fixed costs associated with R&D

investment in other attributes or transactions costs associated with licensing.

Similarly, if the right-hand side is greater than left-hand side, then the licensee

viability and stability conditions provide the relevant constraints upon the feasible

set of equilibrium. Simplifying yields the proportion of sales revenues that licensees

can earn given some level of quality:

As I have assumed , the right-hand side of this condition is nonnegative for

all . Thus, the set of equilibrium configurations derived from the licensor

viability and stability conditions and will be the binding to the feasible

set of equilibrium configurations if:

.

Comparing equation to equation under the assumption that

market size is sufficiently large or fixed R&D and transactions costs are sufficiently

small. The relationship can be specified as:

129

Re-arranging:

As I have already determined that

for condition

to provide the binding set of feasible equilibrium configurations, I know that the

right-hand side of expression will be greatest for

. Substituting and simplifying yields:

As was the case for Proposition 1, the set of equilibrium configurations derived from

the licensor viability and stability conditions and will be the binding

to the feasible set of equilibrium configurations if:

.

130

Proof of Proposition 2: Consider some equilibrium configuration without licensing

in which the market-leading firm produces maximum quality by attaining

maximum competency along some trajectory while producing an “industry

standard” level of competency across all other trajectories. Let the sales revenue

from the associated products be denoted such that its share of industry sales

revenue is . Suppose the high-spending, low-cost entrant produces quality

by attaining capability along trajectory and achieves the “industry

standard” level of competency across all other trajectories.14 By definition of ,

the high-spending entrant obtains a profit net of sunk costs of at least:

.

Recall that the relevant stability condition implies that the profit of an

escalating entrant is non-positive such that:

The viability condition necessitates the current market-leader in quality has

profits that cover its fixed outlays. Thus, regardless of the marginal costs of

production (assumed to be zero here for simplicity and congruency with subsequent

14 The assumption that there is an “industry standard” level of quality offered on all other trajectories is consistent with the results of Irmen and Thisse (1998). They show that maximum differentiation along a single characteristic, and minimum differentiation across all other characteristics, is sufficient to relax price competition, regardless of whether there exists a “dominant” attribute or all attributes are weighted evenly.

131

results), the sales and licensing revenue of the market-leading firm must at least be

as large as its sunk R&D expenditures which implies:

Combining these conditions yields:

Therefore, the market share of sales along the highest-quality trajectory is:

Condition implies that as the market size becomes large (i.e. ), the

second term approaches zero and the market share of the quality-leading firm is

bounded away from zero by

.

Proof of Proposition 3: Consider the case of a high-spending entrant that achieves

competency along some trajectory (with overall quality of ) and licenses

this competency to high-cost rivals. Let the current market leader produce quality

by achieving competency along trajectory , earn sales revenue of the market

leader as , and achieve a share of the industry sales revenue equal to .

By definition of , the high-spending entrant obtains a profit with licensing

132

revenue net of sunk costs of at least:

.

The stability condition for licensor firms implies that the profit of an

escalating entrant is non-positive such that:

Moreover, the relevant viability condition implies that the current quality

leader that licenses its competency to rivals has profits and licensing revenues that

are greater than its fixed R&D costs. The viability condition can be specified as:

Combining equations and and simplifying yields:

The market share of sales for firm producing the highest level of quality and

licensing its competency to high-cost rivals can be expressed as:

133

As the size of the market becomes large, the second term in equation

approaches zero and the lower bound to market concentration derived from the

equilibrium conditions for licensor firms is:

.

Proof of Proposition 4: Consider the case of a high-spending entrant that licenses

competence from the market leader and then escalates its competence by a factor

to attain an overall quality level of . From the definition of , the profits

net of sunk costs and transactions costs associated with licensing for this firm can be

specified as being greater than or equal to:

.

From the stability condition for licensee firms , the profit of an

escalating entrant that licenses competency from the market leader and then

licenses its escalated competency to rivals is non-positive such that:

The viability condition for licensee firms implies that a licensee of the

market-leading competency earns profits that are greater than both the “catch-

134

up” R&D from the imperfect transfer of technologies across firms and the

transactions costs associated with the license . Therefore, sales revenue of the

licensee firm is such that:

Combining the conditions and yields the expression:

Therefore, the market share of any firm producing the market-leading level of

quality and the maximum competency in equilibrium must satisfy:

135

As the size of the market becomes large, the second term approaches zero and the

lower bound to concentration as derived from the equilibrium conditions on

licensee firms is:

.

136

Proof of Theorem 1: (Proof by Transposition) Prior to commencing the proof, it is

useful to recall the three conditions - that were specified in order to

determine which viability and stability conditions characterized the feasible set of

equilibrium configurations. The two licensor conditions can be expressed as:

whereas the licensee condition can be expressed as:

Suppose that the licensee viability and stability conditions are not the

relevant conditions in defining equilibrium configurations implying that equation

does not bind the feasible set of configurations. If equilibrium configurations

are not determined by the licensee conditions, then they must be determined by the

licensor viability condition and one of the licensor stability

conditions, hence either equation or .

137

First, consider the case in which a quality-escalating entrant also licenses its

technology to rivals such that equation is binding. If equation provides

the relevant condition on the binding set of equilibrium configurations, then it must

be that for sufficiently large markets, the right-hand side of is greater than

the right-hand side of . Specifically,

Simplifying equation yields the following expression in which the licensee

conditions are not binding:

Now considering the case in which a quality-escalating entrant does not license its

technology to rivals, equation will define the binding set of feasible

equilibrium configurations. The equivalent expression to equation assuming

sufficiently-sized markets can be specified as:

Dividing both sides by and re-arranging yields the expression:

138

In the Proposition 1, I determined that in order for equation to be binding

relative to equation , it must be that:

. Thus, the

right-hand side of equation is no less than:

.

Simplifying and re-arranging yields the following expression in which the licensee

conditions are not binding:

If the licensee viability and stability conditions are not binding in the definition of

the feasible set of equilibrium configurations, it must be

regardless of which licensor conditions are specified. This is the contra positive to

Theorem 1 implying that if

, it must be that equation

defines the binding set of feasible equilibrium configurations. Moreover, from

Proposition 4 the lower bound to market concentration from the licensee viability

and stability conditions was derived. As these conditions determine the most

restricted set of feasible equilibrium configurations, one can determine that the

139

market share of any firm producing the market-leading level of quality and the

maximum competency in equilibrium must satisfy:

As the size of the market becomes large, the second term approaches zero and the

lower bound to concentration as derived from the equilibrium conditions on

licensee firms is:

.

Proof of Theorem 2: Consider the quality-escalating entrant’s profit derived from the

licensor stability condition is at least:

where is the total number of research trajectories pursued by the innovating

quality leader. The R&D spending of the low-cost quality leader is at least

and it earns sales revenue, separate from licensing revenue, equal to such that

140

the R&D/sales ratio must be at least . We substitute for R&D costs in

equation according to:

Thus, combining inequality with equation yields entrant’s net profit

such that:

The licensor stability condition implies that equation is non-positive.

Re-arranging yields the expression:

From the analysis on the concentration ratios, the sales of the market leader in

quality is at least

, . Thus, one can compare the

coefficient of the first term in expression in order to determine if one would

expect the lower bound to R&D/sales ratio of the quality leader is greater than,

equal to, or less than the lower bound on market concentration. By inspection, the

lower bound on R&D/sales ratio is greater than the lower bound to market

concentration. Substituting for :

141

Thus, as the market size becomes large, the R&D/sales ratio is bounded from below

by

. Under the assumptions over the fixed-fee

royalty payment, , and , the lower bound to the R&D/sales ratio is

strictly greater than the lower bound to market concentration in sales.

142

Appendix B: (Sub-)Market Analysis for GM Crops

Submarket Analysis: State-Level Climate

Figure 16: Average Monthly Temperatures Factor Analysis

Source: Author’s calculations from NOAA data (1970-2000).

Warmer

Cooler No Data

143

Figure 17: Average Monthly Precipitation Factor Analysis (1)

Figure 18: Average Monthly Precipitation Factor Analysis (2)

More

Less No Data

More

Less No Data



144

Figure 19: Average Monthly Drought Likelihood Factor Analysis

Less Prone

More Prone No Data Source: Author’s calculations from NOAA data (1970-2000).

145

Submarket Analysis: Corn

Figure 20: Corn Seed Market Size Factor Analysis

Source: Author’s calculations from Census of Agriculture (1987, 1992).

Larger

Smaller No Data

146

Figure 21: Percentage of Planted Corn Acres Treated with Fertilizer

Figure 22: Percentage of Planted Corn Acres Treated with Herbicide

Source: Author’s calculations from Agricultural Chemical Usage (1990-1995).


More

Less No Data

More

Less No Data

147

Figure 23: Percentage of Planted Corn Acres Treated with Insecticide


More

Less No Data

148

Submarket Analysis: Cotton

Figure 24: Cotton Seed Market Size Factor Analysis


Larger

Smaller No Data

149

Figure 25: Percentage of Planted Cotton Acres Treated with Fertilizer (1)

Figure 26: Percentage of Planted Cotton Acres Treated with Fertilizer (2)


More

Less No Data


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Less No Data

150

Figure 27: Percentage of Planted Cotton Acres Treated with Herbicide

Figure 28: Percentage of Planted Cotton Acres Treated with Insecticide



More

Less No Data

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Less No Data

151

Submarket Analysis: Soybean

Figure 29: Soybean Seed Market Size Factor Analysis


Larger

Smaller No Data

152

Figure 30: Percentage of Planted Soybean Acres Treated with Fertilizer

Figure 31: Percentage of Planted Soybean Acres Treated with Herbicide



More

Less No Data

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Less No Data

153

Figure 32: Percentage of Planted Soybean Acres Treated with Insecticide


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Less No Data

essays on market structure and technological innovation ...import/anderson. 2011... · the...

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